Papers by Jaya Percival Mazorodze
Afrika Matematika, Sep 23, 2023
arXiv (Cornell University), Sep 23, 2023
The atom-bond-connectivity (ABC) index is one of the wellinvestigated degree-based topological in... more The atom-bond-connectivity (ABC) index is one of the wellinvestigated degree-based topological indices. The atom-bond sumconnectivity (ABS) index is a modified version of the ABC index, which was introduced recently. The primary goal of the present paper is to investigate the difference between the aforementioned two indices, namely ABS − ABC. It is shown that the difference ABS − ABC is positive for all graphs of minimum degree at least 2 as well as for all line graphs of those graphs of order at least 5 that are different from the path and cycle graphs. By means of computer search, the difference ABS − ABC is also calculated for all trees of order at most 15.
Journal of Mathematical and Computational Science, Aug 7, 2015
In this paper, we give generalized results of [1], who showed that the best simultaneous approxim... more In this paper, we give generalized results of [1], who showed that the best simultaneous approximation to a set F of uniformly bounded real valued function on [a, b] is equivalent to the best simultaneous approximation of the two functions sup f ∈F f and inf f ∈F f. A simplified proof of this result is also provided.
Journal of Mathematical and Computational Science, Nov 29, 2012
In this paper, we give a simplified proof of the characterization theorem of a one-sided L 1 −app... more In this paper, we give a simplified proof of the characterization theorem of a one-sided L 1 −approximation in [2] and the continuity of the function F → C M (F) (F) in [3].
Afrika Matematika, Jun 11, 2018
Let G be a simple connected, paw-free graph with minimum degree δ, leaf number L(G) and order n. ... more Let G be a simple connected, paw-free graph with minimum degree δ, leaf number L(G) and order n. We show for δ ≥ 3 that L(G) ≥ 1 3 n + 4 3 and the bound is sharp. Further, if G is claw-free, paw-free, we prove for δ ≥ 3 that L(G) ≥ n 2 + 1 2 , and for δ ≥ 5 we prove that L(G) ≥ 4 7 n + 6 7. The results apart from improving some of the results in Griggs et al.
Cornell University - arXiv, Nov 9, 2022
Let d u be the degree of a vertex u of a graph. The atom-bond sum-connectivity (ABS) index of a g... more Let d u be the degree of a vertex u of a graph. The atom-bond sum-connectivity (ABS) index of a graph G is the sum of the numbers (1 − 2(d v + d w) −1) 1/2 over all edges vw of G. This paper gives the characterization of the graphs possessing the minimum ABS index among all trees of a fixed number of pendent vertices. The problem of determining graphs possessing the minimum ABS index in the class of all trees of a fixed order and number of pendent vertices is also addressed, and a partial solution to this problem is provided.
Protesta e indignación global, 2017
Afrika Matematika, 2020
We give an upper bound on the radius of a C 4-free graph in terms order and edge-connectivity. In... more We give an upper bound on the radius of a C 4-free graph in terms order and edge-connectivity. In particular we show that if G is a 3-edge-connected C 4-free graph of order n and radius r , then the inequality r ≤ n 4 + 58 4 holds. Moreover, graphs are constructed to show that the bounds are asymptotically sharp.
Journal of Mathematics, May 4, 2022
For a graph G, its bond incident degree (BID) index is de ned as the sum of the contributions f(d... more For a graph G, its bond incident degree (BID) index is de ned as the sum of the contributions f(d u , d v) over all edges uv of G, where d w denotes the degree of a vertex w of G and f is a real-valued symmetric function. If f(d u , d v) d u + d v or d u d v , then the corresponding BID index is known as the rst Zagreb index M 1 or the second Zagreb index M 2 , respectively. e class of squarehexagonal chains is a subclass of the class of molecular graphs of minimum degree 2. (Formal de nition of a square-hexagonal chain is given in the Introduction section). e present study is motivated from the paper (C. Xiao, H. Chen, Discrete Math. 339 (2016) 506-510) concerning square-hexagonal chains. In the present paper, a general expression for calculating any BID index of square-hexagonal chains is derived. e chains attaining the maximum or minimum values of M 1 and M 2 are also characterized from the class of all square-hexagonal chains having a xed number of polygons.
Journal of Mathematics, 2022
A connected graph in which no edge lies on more than one cycle is called a cactus graph (also kno... more A connected graph in which no edge lies on more than one cycle is called a cactus graph (also known as Husimi tree). A bond incident degree (BID) index of a graph G is defined as ∑ u v ∈ E G f d G u , d G v , where d G w denotes the degree of a vertex w of G , E G is the edge set of G , and f is a real-valued symmetric function. This study involves extremal results of cactus graphs concerning the following type of the BID indices: I f i G = ∑ u v ∈ E G f i d G u / d G u + f i d G v / d G v , where i ∈ 1,2 , f 1 is a strictly convex function, and f 2 is a strictly concave function. More precisely, graphs attaining the minimum and maximum I f i values are studied in the class of all cactus graphs with a given number of vertices and cycles. The obtained results cover several well-known indices including the general zeroth-order Randić index, multiplicative first and second Zagreb indices, and variable sum exdeg index.
La Matematica, 2022
Let G be a simple, connected, triangle-free graph with minimum degree δ, order n and leaf number ... more Let G be a simple, connected, triangle-free graph with minimum degree δ, order n and leaf number L(G). If G has a cut-vertex, we prove that L(G) ≥ 4δ − 4 and n ≥ 4δ − 1. Both lower bounds are sharp. The lower bound on the leaf number strengthens a result by Mukwembi for triangle-free graphs. As corollaries, we deduce sufficient conditions for connectivity, traceability and Hamiltonicity in triangle-free graphs. As an easy extension of a result by Goodman and Hedetiniemi, we show that a simple, connected, claw-free, paw-free graph G is Hamiltonian if and only if G is not a path. We consider only simple graphs, that is, graphs with neither loops nor multiple edges.
Transactions on Combinatorics, 2020
We study the Gutman index ${rm Gut}(G)$ and the edge-Wiener index $W_e (G)$ of connected graphs ... more We study the Gutman index ${rm Gut}(G)$ and the edge-Wiener index $W_e (G)$ of connected graphs $G$ of given order $n$ and edge-connectivity $lambda$. We show that the bound ${rm Gut}(G) le frac{2^4 cdot 3}{5^5 (lambda+1)} n^5 + O(n^4)$ is asymptotically tight for $lambda ge 8$. We improve this result considerably for $lambda le 7$ by presenting asymptotically tight upper bounds on ${rm Gut}(G)$ and $W_e (G)$ for $2 le lambda le 7$.
This thesis details the results of an investigation of bounds on four distances measures, namely,... more This thesis details the results of an investigation of bounds on four distances measures, namely, radius, diameter, the Gutman index and the edge-Wiener index, in terms of other graph parameters, namely, order, irregularity index and the three classical connectivity measures, minimum degree, vertex-connectivity and edgeconnectivity. The thesis has six chapters. In Chapter 1, we de ne the most important terms used throughout the thesis and we also give a motivation for our research and provide background for relevant results. In this chapter we include the importance of the distance measures to be studied.Chapter 2 focuses on the radius, diameter and the degree sequence of a graph. We give asymptotically sharp upper bounds on the radius and diameter of (i) a connected graph, (ii) a connected triangle-free graph, (iii) a connected C4-free graph of given order, minimum degree, and given number of distinct terms in the degree sequence of the graph. We also give better bounds for graphs ...
International Journal of Mathematics and Mathematical Sciences, 2020
We present upper bounds on the diameter of bipartite and triangle-free graphs with prescribed edg... more We present upper bounds on the diameter of bipartite and triangle-free graphs with prescribed edge connectivity with respect to order and size. All bounds presented in this paper are asymptotically sharp.
Journal of Mathematics, 2020
We show that if G is a 3-vertex-connected C4-free graph of order n and radius r, then the inequal... more We show that if G is a 3-vertex-connected C4-free graph of order n and radius r, then the inequality r≤2n/9+O1 holds. Moreover, graphs are constructed to show that the bounds are asymptotically sharp.
Acta Mathematica Hungarica, 2017
To bound the size (the number of edges) of a graph in terms of other parameters of a graph forms ... more To bound the size (the number of edges) of a graph in terms of other parameters of a graph forms an important family of problems in the extremal graph theory. We present a number of upper bounds on the size of general graphs and triangle-free graphs. We bound the size of any graph and of any triangle-free graph in terms of its order (number of vertices), diameter and edge-connectivity. We also give an upper bound on the size of triangle-free graphs of given order, diameter and minimum degree. All bounds presented in this paper are asymptotically sharp.
Mathematica Slovaca, 2015
We give asymptotically sharp upper bounds on the radius and diameter of (i) a connected graph, (i... more We give asymptotically sharp upper bounds on the radius and diameter of (i) a connected graph, (ii) a connected triangle-free graph, (iii) a connected C4-free graph of given order, minimum degree, and maximum degree. We also give better bounds on the radius and diameter for triangle-free graphs with a given order, minimum degree and a given number of distinct terms in the degree sequence of the graph. Our results improve on old classical theorems by Erd˝os, Pach, Pollack and Tuza [Radius, diameter, and minimum degree, J. Combin. Theory Ser. B 47 (1989), 73-79] on radius, diameter and minimum degree.
Discussiones Mathematicae Graph Theory, 2016
The Gutman index and the edge-Wiener index have been extensively investigated particularly in the... more The Gutman index and the edge-Wiener index have been extensively investigated particularly in the last decade. An important stream of research on graph indices is to bound indices in terms of the order and other parameters of given graph. In this paper we present asymptotically sharp upper bounds on the Gutman index and the edge-Wiener index for graphs of given order and vertex-connectivity κ, where κ is a constant. Our results substantially generalize and extend known results in the area.
Indian Journal of Pure and Applied Mathematics, 2020
We give an upper bound on the diameter of a 3-edge-connected C4-free graph in terms of order. In ... more We give an upper bound on the diameter of a 3-edge-connected C4-free graph in terms of order. In particular we show that if G is a 3-edge-connected C4 free graph of order n, and diameter d, then the inequality $$d \le {{3n} \over 7} — {3 \over 7}$$ holds. Moreover, graphs are constructed to show that the bound is almost asymptotically sharp.
Uploads
Papers by Jaya Percival Mazorodze