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Sudev Naduvath

Christ University, Bangalore, India, Mathematics, Faculty Member

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I am working as an Associate Professor in the Department of Mathematics in Christ University, Bangalore, India.
Phone: +919497557876
Address: Department of Mathematics,
Vidya Academy of Science and Technology,
Thalakkootukara. P. O.,
Thrissur-680501,
Kerala, India

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Dr. V. Yegnanarayanan MATHS

Antonio Iovanella

UNINT Università degli Studi Internazionali di Roma

Denae Ventura Arredondo

University of California, Davis

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Papers by Sudev Naduvath

Jaco-type graphs and black energy dissipation

Advances in Pure and Applied Mathematics, 2017

In this paper, we introduce the notion of an energy graph

Topological Integer Additive Set-Graceful Graphs

International Journal of Computer Applications, 2015

Let N 0 denote the set of all non-negative integers and X be any subset of X. Also denote the pow... more Let N 0 denote the set of all non-negative integers and X be any subset of X. Also denote the power set of X by P(X). An integer additive set-labeling (IASL) of a graph G is an injective function f : V (G) → P(X) such that the induced function f + : E(G) → P(X) is defined by f + (uv) = f (u) + f (v), where f (u) + f (v) is the sumset of f (u) and f (v). An IASL f is said to be a topological IASL (Top-IASL) if f (V (G)) ∪ {∅} is a topology of the ground set X. An IASL is said to be an integer additive set-graceful labeling (IASGL) if for the induced edgefunction f + , f + (E(G)) = P(X) − {∅, {0}}. In this paper, we study certain types of IASL of a given graph G, which is a topological integer additive set-labeling as well as an integer additive set-graceful labeling of G.

Further Studies on the Sparing Number of Graphs

Let $\mathbb{N}_0$ denote the set of all non-negative integers and $\mathcal{P}(\mathbb{N}_0)$ be... more Let $\mathbb{N}_0$ denote the set of all non-negative integers and $\mathcal{P}(\mathbb{N}_0)$ be its power set. An integer additive set-indexer is an injective function $f:V(G)\to \mathcal{P}(\mathbb{N}_0)$ such that the induced function $f^+:E(G) \to \mathcal{P}(\mathbb{N}_0)$ defined by $f^+ (uv) = f(u)+ f(v)$ is also injective, where $f(u)+f(v)$ is the sum set of $f(u)$ and $f(v)$. If $f^+(uv)=k~\forall~uv\in E(G)$, then $f$ is said to be a $k$-uniform integer additive set-indexer. An integer additive set-indexer $f$ is said to be a weak integer additive set-indexer if $|f^+(uv)|=\max(|f(u)|,|f(v)|)~\forall ~ uv\in E(G)$. In this paper, we study the admissibility of weak integer additive set-indexer by certain graphs and graph operations.

Injective coloring parameters of some special classes of graphs

The vertex coloring of a graph can be viewed as a random experiment and with respect to this expe... more The vertex coloring of a graph can be viewed as a random experiment and with respect to this experiment, a random variable X can be defined such that X denotes the color of an arbitrarily chosen vertex. In this paper, we broaden the ideas of coloring mean and variance of graphs with respect to a particular type of proper injective coloring and determine these parameters for some standard graph classes.

On Star Decomposition and Star Number of Some Graph Classes

HAL (Le Centre pour la Communication Scientifique Directe), Dec 31, 2018

HAL is a multidisciplinary open access archive for the deposit and dissemination of scientific re... more HAL is a multidisciplinary open access archive for the deposit and dissemination of scientific research documents, whether they are published or not. The documents may come from teaching and research institutions in France or abroad, or from public or private research centers. L'archive ouverte pluridisciplinaire HAL, est destinée au dépôt et à la diffusion de documents scientifiques de niveau recherche, publiés ou non, émanant des établissements d'enseignement et de recherche français ou étrangers, des laboratoires publics ou privés.

A Note On The Sparing Number Of The Sieve Graphs Of Certain Graphs

Le Centre pour la Communication Scientifique Directe - HAL - memSIC, May 11, 2015

Let N0 denote the set of all non-negative integers and P(N0) be its power set. An integer additiv... more Let N0 denote the set of all non-negative integers and P(N0) be its power set. An integer additive set-indexer (IASI) of a given graph G is an injective function f : V (G) → P(N0) such that the induced function f + : E(G) → P(N0) defined by f + (uv) = f (u) + f (v) is also injective. An IASI f of a graph G is said to be a weak IASI of G if |f + (uv)| = max(|f (u)|, |f (v)|) for all u, v ∈ V (G). A graph which admits a weak IASI may be called a weak IASI graph. The sparing number of a graph G is the minimum number of edges with singleton set-labels required for a graph G to admit a weak IASI. In this paper, we introduce the notion of k-sieve graphs of a given graph and study their sparing numbers.

On -Coloring Parameters of Some Classes of Graphs

Le Centre pour la Communication Scientifique Directe - HAL - Archive ouverte HAL, Sep 2, 2019

Vertex coloring has always been a topic of interest. Motivated by the studies on-chromatic mean a... more Vertex coloring has always been a topic of interest. Motivated by the studies on-chromatic mean and variance of some standard graphs, in this paper, we obtain few results for-chromatic and +-chromatic mean and variance of some cycle related graph classes. Here, Vertex coloring of a graph is taken to be the random experiment. Discrete random variable for this random experiment is the color of randomly chosen vertex of .

A study on set-cordial labeling of graphs

Communications Faculty Of Science University of Ankara Series A1Mathematics and Statistics

For a non-empty ground set XX, finite or infinite, the set-valuation or set-labeling of a given g... more For a non-empty ground set XX, finite or infinite, the set-valuation or set-labeling of a given graph GG is an injective function f:V(G)→P(X)f:V(G)→P(X), where P(X)P(X) is the power set of the set XX. In this paper, we introduce a new type of set-labeling, called set-cordial labeling and study the characteristics of graphs which admit the set-cordial labeling.

On δ(k)-coloring of powers of helm and closed helm graphs

Discrete Mathematics, Algorithms and Applications, 2021

If the availability of colors to color a graph [Formula: see text] is less than that of the chrom... more If the availability of colors to color a graph [Formula: see text] is less than that of the chromatic number [Formula: see text] of the graph, then coloring the graph with available colors, say [Formula: see text] colors, where [Formula: see text], will cause the end vertices of at least one edge to be colored with same color. Such an edge whose end vertices receive a same color is called as a bad edge. A coloring that restricts few color classes to have adjacency between the elements in it so as to minimize the number of bad edges obtained from it in a graph [Formula: see text] is called as a near proper coloring and a near proper coloring that uses [Formula: see text] colors where [Formula: see text] to color a graph [Formula: see text] by permitting only one color class to have adjacency among the elements in it and thereby minimize the number of bad edges resulting from the permitted color class is called as a [Formula: see text]-coloring of the graph [Formula: see text]. In thi...

Graphs and Their Sumset Valuations

A Study on Integer Additive Set-Labeled Graphs

Fundamentals of calculus

Vertex stress related parameters for certain Kneser graphs

Acta Universitatis Sapientiae, Informatica, 2021

This paper presents results for some vertex stress related parameters in respect of specific subf... more This paper presents results for some vertex stress related parameters in respect of specific subfamilies of Kneser graphs. Kneser graphs for which diam(KG(n, k)) = 2 and k ≥ 2 are considered. The note establishes the foundation for researching similar results for Kneser graphs for which diam(KG(n, k)) ≥ 3. In addition some important vertex stress related properties are stated. Finally some results for specific bipartite Kneser graphs i.e. BK(n, 1), n ≥ 3 will be presented. In the conclusion some worthy research avenues are proposed.

A Study on Jaco-Type Graphs

Journal of Informatics and Mathematical Sciences, 2016

For a sequence \(\{a_n\}\) in general such that \(a_n \in \mathbb{N}\) and \(a_{n+1}\ge a_n\), \(... more For a sequence \(\{a_n\}\) in general such that \(a_n \in \mathbb{N}\) and \(a_{n+1}\ge a_n\), \(n=1,2,3,\ldots\), a new population of directed graphs is defined such that for a given sequence \(\{a_n\}\) the infinite directed root -graph has \(d^+(v_n)=a_n\). The infinite directed root -graph is denoted \(J_\infty(\{a_n\})\). The family of finite Jaco-Type graphs is the set of directed graphs \(J_n(\{a_n\})\), \(n\in \mathbb{N}\) by lobbing off all vertices and arcs in \(J_\infty(\{a_n\})\) for vertices \(v_i\), \(i > n\). We present introductory results for two families of these new directed graphs.

ANoteonMcPhersonNumberofGraphs Research Article

By the explosion of a vertex v in a graph G, we mean drawing edges from v to all other vertices i... more By the explosion of a vertex v in a graph G, we mean drawing edges from v to all other vertices in G that are not already adjacent to it. The recursive concept of vertex explosions is called the McPherson recursion. The McPherson number of a graph is the minimum number of vertex explosions required in G so that the resultant graph becomes a complete graph. In this paper, we determine the McPherson number of a given graph.

Curling Sub-sequences and Curling Number of Certain Graphs

arXiv: Combinatorics, 2015

In this paper, we introduce the concept of curling subsequence of simple, finite and connected gr... more In this paper, we introduce the concept of curling subsequence of simple, finite and connected graphs. A curling subsequence is a maximal subsequence $C$ of the degree sequence of a simple connected graph $G$ for which the curling number $cn(G)$ corresponds to the curling number of the degree sequence per se and hence we call it the curling number of the graph $G$. A maximal degree subsequence with equal entries is called an identity subsequence. The number of identity curling subsequences in a simple connected graph $G$ is denoted $ic(G).$ We show that the curling number conjecture holds for the degree sequence of a simple connected graph $G$ on $n \geq 1$ vertices. We also introduce the notion of the compound curling number of a simple connected graph $G$ and then initiate a study on the curling number of Jaco graphs.

On Integer Additive Set-Valuations of Finite Jaco Graphs

Journal of Informatics and Mathematical Sciences, 2016

Let \(X\) denote a set of non-negative integers and \(\mathcal{P}(X)\) be its power set. An integ... more Let \(X\) denote a set of non-negative integers and \(\mathcal{P}(X)\) be its power set. An integer additive set-labeling (IASL) of a graph \(G\) is an injective set-valued function \(f:V(G)\to \mathcal{P}(X)-\{\emptyset\}\) where induced function \(f^+:E(G) \to \mathcal{P}(X)-\{\emptyset\}\) is defined by \(f^+ (uv) = f(u)+ f(v)\), where \(f(u)+f(v)\) is the sumset of \(f(u)\) and \(f(v)\). Let \(f(x)=mx+c\); \(m\in \mathbb{N}\), \(c\in N_0\). A finite linear Jaco graph, denoted by \(J_n(f(x))\), is a directed graph with vertex set \(\{v_i: i\in \mathbb{N}\}\) such that \((v_i,v_j)\) is an arc of \(J_n(f(x))\) if and only if \(f(i)+i-d^-(v_j)\ge j\). In this paper, we discuss the admissibility of different types of integer additive set-labeling by finite linear Jaco graphs.

Modular Sumset Labelling of Graphs

Graph labelling is an assignment of labels or weights to the vertices and/or edges of a graph. Fo... more Graph labelling is an assignment of labels or weights to the vertices and/or edges of a graph. For a ground set X of integers, a sumset labelling of a graph is an injective map f:VG→PX such that the induced function f⊕:EG→PX is defined by f+uv=fu+fv, for all uv∈EG, where fu+fv is the sumset of the set-label, the vertices u and v. In this chapter, we discuss a special type of sumset labelling of a graph, called modular sumset labelling and its variations. We also discuss some interesting characteristics and structural properties of the graphs which admit these new types of graph labellings.

On Associated Graphs of Arithmetic IASI Graphs

A note on δ^(k)-colouring of the Cartesian product of some graphs

The chromatic number, Χ(G) of a graph G is the minimum number of colours used in a proper colouri... more The chromatic number, Χ(G) of a graph G is the minimum number of colours used in a proper colouring of G. In improper colouring, an edge uv is bad if the colours assigned to the end vertices of the edge is the same. Now, if the available colours are less than that of the chromatic number of graph G, then colouring the graph with the available colours leads to bad edges in G. The number of bad edges resulting from a δ(k)-colouring of G is denoted by bk(G). In this paper, we use the concept of δ(k)-colouring and determine the number of bad edges in the Cartesian product of some graphs.

Jaco-type graphs and black energy dissipation

Advances in Pure and Applied Mathematics, 2017

In this paper, we introduce the notion of an energy graph

Topological Integer Additive Set-Graceful Graphs

International Journal of Computer Applications, 2015

Let N 0 denote the set of all non-negative integers and X be any subset of X. Also denote the pow... more Let N 0 denote the set of all non-negative integers and X be any subset of X. Also denote the power set of X by P(X). An integer additive set-labeling (IASL) of a graph G is an injective function f : V (G) → P(X) such that the induced function f + : E(G) → P(X) is defined by f + (uv) = f (u) + f (v), where f (u) + f (v) is the sumset of f (u) and f (v). An IASL f is said to be a topological IASL (Top-IASL) if f (V (G)) ∪ {∅} is a topology of the ground set X. An IASL is said to be an integer additive set-graceful labeling (IASGL) if for the induced edgefunction f + , f + (E(G)) = P(X) − {∅, {0}}. In this paper, we study certain types of IASL of a given graph G, which is a topological integer additive set-labeling as well as an integer additive set-graceful labeling of G.

Further Studies on the Sparing Number of Graphs

Let $\mathbb{N}_0$ denote the set of all non-negative integers and $\mathcal{P}(\mathbb{N}_0)$ be... more Let $\mathbb{N}_0$ denote the set of all non-negative integers and $\mathcal{P}(\mathbb{N}_0)$ be its power set. An integer additive set-indexer is an injective function $f:V(G)\to \mathcal{P}(\mathbb{N}_0)$ such that the induced function $f^+:E(G) \to \mathcal{P}(\mathbb{N}_0)$ defined by $f^+ (uv) = f(u)+ f(v)$ is also injective, where $f(u)+f(v)$ is the sum set of $f(u)$ and $f(v)$. If $f^+(uv)=k~\forall~uv\in E(G)$, then $f$ is said to be a $k$-uniform integer additive set-indexer. An integer additive set-indexer $f$ is said to be a weak integer additive set-indexer if $|f^+(uv)|=\max(|f(u)|,|f(v)|)~\forall ~ uv\in E(G)$. In this paper, we study the admissibility of weak integer additive set-indexer by certain graphs and graph operations.

Injective coloring parameters of some special classes of graphs

The vertex coloring of a graph can be viewed as a random experiment and with respect to this expe... more The vertex coloring of a graph can be viewed as a random experiment and with respect to this experiment, a random variable X can be defined such that X denotes the color of an arbitrarily chosen vertex. In this paper, we broaden the ideas of coloring mean and variance of graphs with respect to a particular type of proper injective coloring and determine these parameters for some standard graph classes.

On Star Decomposition and Star Number of Some Graph Classes

HAL (Le Centre pour la Communication Scientifique Directe), Dec 31, 2018

HAL is a multidisciplinary open access archive for the deposit and dissemination of scientific re... more HAL is a multidisciplinary open access archive for the deposit and dissemination of scientific research documents, whether they are published or not. The documents may come from teaching and research institutions in France or abroad, or from public or private research centers. L'archive ouverte pluridisciplinaire HAL, est destinée au dépôt et à la diffusion de documents scientifiques de niveau recherche, publiés ou non, émanant des établissements d'enseignement et de recherche français ou étrangers, des laboratoires publics ou privés.

A Note On The Sparing Number Of The Sieve Graphs Of Certain Graphs

Le Centre pour la Communication Scientifique Directe - HAL - memSIC, May 11, 2015

Let N0 denote the set of all non-negative integers and P(N0) be its power set. An integer additiv... more Let N0 denote the set of all non-negative integers and P(N0) be its power set. An integer additive set-indexer (IASI) of a given graph G is an injective function f : V (G) → P(N0) such that the induced function f + : E(G) → P(N0) defined by f + (uv) = f (u) + f (v) is also injective. An IASI f of a graph G is said to be a weak IASI of G if |f + (uv)| = max(|f (u)|, |f (v)|) for all u, v ∈ V (G). A graph which admits a weak IASI may be called a weak IASI graph. The sparing number of a graph G is the minimum number of edges with singleton set-labels required for a graph G to admit a weak IASI. In this paper, we introduce the notion of k-sieve graphs of a given graph and study their sparing numbers.

On -Coloring Parameters of Some Classes of Graphs

Le Centre pour la Communication Scientifique Directe - HAL - Archive ouverte HAL, Sep 2, 2019

Vertex coloring has always been a topic of interest. Motivated by the studies on-chromatic mean a... more Vertex coloring has always been a topic of interest. Motivated by the studies on-chromatic mean and variance of some standard graphs, in this paper, we obtain few results for-chromatic and +-chromatic mean and variance of some cycle related graph classes. Here, Vertex coloring of a graph is taken to be the random experiment. Discrete random variable for this random experiment is the color of randomly chosen vertex of .

A study on set-cordial labeling of graphs

Communications Faculty Of Science University of Ankara Series A1Mathematics and Statistics

For a non-empty ground set XX, finite or infinite, the set-valuation or set-labeling of a given g... more For a non-empty ground set XX, finite or infinite, the set-valuation or set-labeling of a given graph GG is an injective function f:V(G)→P(X)f:V(G)→P(X), where P(X)P(X) is the power set of the set XX. In this paper, we introduce a new type of set-labeling, called set-cordial labeling and study the characteristics of graphs which admit the set-cordial labeling.

On δ(k)-coloring of powers of helm and closed helm graphs

Discrete Mathematics, Algorithms and Applications, 2021

If the availability of colors to color a graph [Formula: see text] is less than that of the chrom... more If the availability of colors to color a graph [Formula: see text] is less than that of the chromatic number [Formula: see text] of the graph, then coloring the graph with available colors, say [Formula: see text] colors, where [Formula: see text], will cause the end vertices of at least one edge to be colored with same color. Such an edge whose end vertices receive a same color is called as a bad edge. A coloring that restricts few color classes to have adjacency between the elements in it so as to minimize the number of bad edges obtained from it in a graph [Formula: see text] is called as a near proper coloring and a near proper coloring that uses [Formula: see text] colors where [Formula: see text] to color a graph [Formula: see text] by permitting only one color class to have adjacency among the elements in it and thereby minimize the number of bad edges resulting from the permitted color class is called as a [Formula: see text]-coloring of the graph [Formula: see text]. In thi...

Graphs and Their Sumset Valuations

A Study on Integer Additive Set-Labeled Graphs

Fundamentals of calculus

Vertex stress related parameters for certain Kneser graphs

Acta Universitatis Sapientiae, Informatica, 2021

This paper presents results for some vertex stress related parameters in respect of specific subf... more This paper presents results for some vertex stress related parameters in respect of specific subfamilies of Kneser graphs. Kneser graphs for which diam(KG(n, k)) = 2 and k ≥ 2 are considered. The note establishes the foundation for researching similar results for Kneser graphs for which diam(KG(n, k)) ≥ 3. In addition some important vertex stress related properties are stated. Finally some results for specific bipartite Kneser graphs i.e. BK(n, 1), n ≥ 3 will be presented. In the conclusion some worthy research avenues are proposed.

A Study on Jaco-Type Graphs

Journal of Informatics and Mathematical Sciences, 2016

For a sequence \(\{a_n\}\) in general such that \(a_n \in \mathbb{N}\) and \(a_{n+1}\ge a_n\), \(... more For a sequence \(\{a_n\}\) in general such that \(a_n \in \mathbb{N}\) and \(a_{n+1}\ge a_n\), \(n=1,2,3,\ldots\), a new population of directed graphs is defined such that for a given sequence \(\{a_n\}\) the infinite directed root -graph has \(d^+(v_n)=a_n\). The infinite directed root -graph is denoted \(J_\infty(\{a_n\})\). The family of finite Jaco-Type graphs is the set of directed graphs \(J_n(\{a_n\})\), \(n\in \mathbb{N}\) by lobbing off all vertices and arcs in \(J_\infty(\{a_n\})\) for vertices \(v_i\), \(i > n\). We present introductory results for two families of these new directed graphs.

ANoteonMcPhersonNumberofGraphs Research Article

By the explosion of a vertex v in a graph G, we mean drawing edges from v to all other vertices i... more By the explosion of a vertex v in a graph G, we mean drawing edges from v to all other vertices in G that are not already adjacent to it. The recursive concept of vertex explosions is called the McPherson recursion. The McPherson number of a graph is the minimum number of vertex explosions required in G so that the resultant graph becomes a complete graph. In this paper, we determine the McPherson number of a given graph.

Curling Sub-sequences and Curling Number of Certain Graphs

arXiv: Combinatorics, 2015

In this paper, we introduce the concept of curling subsequence of simple, finite and connected gr... more In this paper, we introduce the concept of curling subsequence of simple, finite and connected graphs. A curling subsequence is a maximal subsequence $C$ of the degree sequence of a simple connected graph $G$ for which the curling number $cn(G)$ corresponds to the curling number of the degree sequence per se and hence we call it the curling number of the graph $G$. A maximal degree subsequence with equal entries is called an identity subsequence. The number of identity curling subsequences in a simple connected graph $G$ is denoted $ic(G).$ We show that the curling number conjecture holds for the degree sequence of a simple connected graph $G$ on $n \geq 1$ vertices. We also introduce the notion of the compound curling number of a simple connected graph $G$ and then initiate a study on the curling number of Jaco graphs.

On Integer Additive Set-Valuations of Finite Jaco Graphs

Journal of Informatics and Mathematical Sciences, 2016

Let \(X\) denote a set of non-negative integers and \(\mathcal{P}(X)\) be its power set. An integ... more Let \(X\) denote a set of non-negative integers and \(\mathcal{P}(X)\) be its power set. An integer additive set-labeling (IASL) of a graph \(G\) is an injective set-valued function \(f:V(G)\to \mathcal{P}(X)-\{\emptyset\}\) where induced function \(f^+:E(G) \to \mathcal{P}(X)-\{\emptyset\}\) is defined by \(f^+ (uv) = f(u)+ f(v)\), where \(f(u)+f(v)\) is the sumset of \(f(u)\) and \(f(v)\). Let \(f(x)=mx+c\); \(m\in \mathbb{N}\), \(c\in N_0\). A finite linear Jaco graph, denoted by \(J_n(f(x))\), is a directed graph with vertex set \(\{v_i: i\in \mathbb{N}\}\) such that \((v_i,v_j)\) is an arc of \(J_n(f(x))\) if and only if \(f(i)+i-d^-(v_j)\ge j\). In this paper, we discuss the admissibility of different types of integer additive set-labeling by finite linear Jaco graphs.

Modular Sumset Labelling of Graphs

Graph labelling is an assignment of labels or weights to the vertices and/or edges of a graph. Fo... more Graph labelling is an assignment of labels or weights to the vertices and/or edges of a graph. For a ground set X of integers, a sumset labelling of a graph is an injective map f:VG→PX such that the induced function f⊕:EG→PX is defined by f+uv=fu+fv, for all uv∈EG, where fu+fv is the sumset of the set-label, the vertices u and v. In this chapter, we discuss a special type of sumset labelling of a graph, called modular sumset labelling and its variations. We also discuss some interesting characteristics and structural properties of the graphs which admit these new types of graph labellings.

On Associated Graphs of Arithmetic IASI Graphs

A note on δ^(k)-colouring of the Cartesian product of some graphs

The chromatic number, Χ(G) of a graph G is the minimum number of colours used in a proper colouri... more The chromatic number, Χ(G) of a graph G is the minimum number of colours used in a proper colouring of G. In improper colouring, an edge uv is bad if the colours assigned to the end vertices of the edge is the same. Now, if the available colours are less than that of the chromatic number of graph G, then colouring the graph with the available colours leads to bad edges in G. The number of bad edges resulting from a δ(k)-colouring of G is denoted by bk(G). In this paper, we use the concept of δ(k)-colouring and determine the number of bad edges in the Cartesian product of some graphs.