Papers by Venkanagouda Goudar
JNNCE Journal of Engineering &Managment, Jan 31, 2022
Let G = (p, q) be a connected graph and Me(G) be its corresponding edge semi-middle graph. A domi... more Let G = (p, q) be a connected graph and Me(G) be its corresponding edge semi-middle graph. A dominating set D ⊆ V [Me(G)] is split dominating set V [Me(G)] − D is disconnected. The minimum size of D is called the split domination number of Me(G) and is denoted by γs[Me(G)]. In this paper we obtain several results on split domination number.
Malaya journal of matematik, 2019
Global Journal of Science Frontier Research, Feb 28, 2013
ABSTRACT In this communucations, the concept of semirelib cutvertex graph of a planar graph is in... more ABSTRACT In this communucations, the concept of semirelib cutvertex graph of a planar graph is introduced. We presen a characterization of those graphs whose semirelib cutvertex graphs are planar, outer planar, eulerian, hamiltonian with crossing number one.
Malaya journal of matematik, 2020
In this communication, the pathos edge semi-middle graph of a tree is introduced. Its study is co... more In this communication, the pathos edge semi-middle graph of a tree is introduced. Its study is concentrated only on trees. We present a characterization of those graphs whose pathos edge semi-middle graph of a tree is planar, outerplanar and minimally nonouterplanar. Further, Also we establish a characterization of graphs whose pathos edge semi-middle graph of a trees are noneularian, hamiltonian and the graphs whose crossing number one and two.
Applied mathematical sciences, 2013
International Journal of Mathematics Trends and Technology, Apr 25, 2022
International journal of statistics and applied mathematics, Jul 1, 2022
Let (,) be a connected graph and () be its corresponding vertex semi middle graph. A dominating s... more Let (,) be a connected graph and () be its corresponding vertex semi middle graph. A dominating set ⊆ [ ()] is Nonsplit dominating set 〈 [ ()] − 〉 is connected. The minimum size of D is called the Nonsplit domination number of () and is denoted by [ ()]. In this paper we obtain several results on Nonsplit domination number.
International journal of computer applications, Aug 17, 2017
For any graph G(V, E), the line graph of G denoted by L(G). The Line graph L(G) whose vertices co... more For any graph G(V, E), the line graph of G denoted by L(G). The Line graph L(G) whose vertices corresponds to the edges of G and two vertices in L(G) are adjacent if and only if the corresponding edges in G are adjacent. A geodetic set S ⊆ V (G) of a graph G = (V, E) is a restrained geodetic set if the subgraph V − S has no isolated vertex. The minimum cardinality of a restrained geodetic set is the restrained geodetic number. In this paper we obtained the restrained geodetic number of line graph of any graph. Also, obtained many bounds on restrained geodetic number in terms of elements of G and covering number of G.
Pan-American Journal of Mathematics
Let G = (p, q) be a connected graph and Me(G) be its corresponding edge semi-middle graph. A domi... more Let G = (p, q) be a connected graph and Me(G) be its corresponding edge semi-middle graph. A dominating set D ⊆ V [Me(G)] is split dominating set V [Me(G)] – D is disconnected. The minimum size of D is called the split domination number of Me(G) and is denoted by γs[Me(G)]. In this paper we obtain several results on split domination number.
JNNCE Journal of Engineering and Management, 2022
A graph is said to be planar if it can be drawn on the plane without any of its edges intersectin... more A graph is said to be planar if it can be drawn on the plane without any of its edges intersecting. A planar graph is outerplanar. IIf all of its vertices are on the exterior region, it can be embedded in the plane. The concept of a minimally nonouterplanar graph is first described in [3]. When considering a planar graph G, the inner vertex number i(G) is defined as the minimum possible number of vertices that do not belong to either the boundary of the exterior region or any of the boundaries of G in the plane. Assuming that i(G) = 0, then G is clearly planar. If i(G)=1, then a graph G is minimally nonouterplanar and G is k-minimally nonouterplanar (k≥2) if i(G)=k.
ACS Applied Materials & Interfaces, 2021
Three-dimensional (3D) spheroid culture provides opportunities to model tumor growth closer to it... more Three-dimensional (3D) spheroid culture provides opportunities to model tumor growth closer to its natural context. The collagen network in the extracellular matrix supports autonomic tumor cell proliferation, but its presence and role in tumor spheroids remain unclear. In this research, we developed an in vitro 3D co-culture model in a microwell 3D (μ-well 3D) cell-culture array platform to mimic the tumor microenvironment (TME). The modular setup is used to characterize the paracrine signaling molecules and the role of the intraspheroidal collagen network in cancer drug resistance. The μ-well 3D platform is made up of poly(dimethylsiloxane) that contains 630 round wells for individual spheroid growth. Inside each well, the growth surface measured 500 μm in diameter and was functionalized with the amphiphilic copolymer. HCT-8 colon cancer cells and/or NIH3T3 fibroblasts were seeded in each well and incubated for up to 9 days for TME studies. It was observed that NIH3T3 cells promoted the kinetics of tumor organoid formation. The two types of cells self-organized into core-shell chimeric tumor spheroids (CTSs) with fibroblasts confined to the shell and cancer cells localized to the core. Confocal microscopy analysis indicated that a type-I collagen network developed inside the CTS along with increased TGF-β1 and α-SMA proteins. The results were correlated with a significantly increased stiffness in 3D co-cultured CTS up to 52 kPa as compared to two-dimensional (2D) co-culture. CTS was more resistant to 5-FU (IC50 = 14.0 ± 3.9 μM) and Regorafenib (IC50 = 49.8 ± 9.9 μM) compared to cells grown under the 2D condition 5-FU (IC50 = 12.2 ± 3.7 μM) and Regorafenib (IC50 = 5.9 ± 1.9 μM). Targeted collagen homeostasis with Sclerotiorin led to damaged collagen structure and disrupted the type-I collagen network within CTS. Such a treatment significantly sensitized collagen-supported CTS to 5-FU (IC50 = 4.4 ± 1.3 μM) and to Regorafenib (IC50 = 0.5 ± 0.2 μM). In summary, the efficient formation of colon cancer CTSs in a μ-well 3D culture platform allows exploration of the desmoplastic TME. The novel role of intratumor collagen quality as a drug sensitization target warrants further investigation.
In this paper we obtain the split geodetic number of line graph of any graph. Also obtain many bo... more In this paper we obtain the split geodetic number of line graph of any graph. Also obtain many bounds on split geodetic number in terms of elements of G and covering number of G. We also investigate the relationship between split geodetic number and geodetic number.
A set S ⊆ V (G) is a split geodetic set of G, if S is a geode-tic set and 〈V − S 〉 is disconnecte... more A set S ⊆ V (G) is a split geodetic set of G, if S is a geode-tic set and 〈V − S 〉 is disconnected. The split geodetic number of a graph G, is denoted by gs(G), is the minimum cardinality of a split geodetic set of G. A set S ⊆ V (G) is a strong split geodetic set of G, if S is a geodetic set and 〈V − S 〉 is totally disconnected. The strong split geodetic number of a graph G, is denoted by gss(G), is the minimum cardinality of a strong split geodetic set of G. In this paper we obtain the geodetic number, split geodetic number, strong split geodetic number and non split geodetic number of strong product graphs, composition of graphs and join of graphs. Keywords:
A set F of a graph is an edge dominating set if every edge in is adjacent to some edge in F. An e... more A set F of a graph is an edge dominating set if every edge in is adjacent to some edge in F. An edge domination number of G is the minimum cardinality of an edge dominating set. An edge dominating set F is called a doubly connected edge dominating set if the induced subgraphs and are connected. The minimum cardinality of the doubly connected edge dominating set in G is its domination number and is denoted by We study the graph theoretic properties of and its exact values for some standard graphs. The relation between with other parameters is also investigated.
A set F of a graph G(V, E) is an edge dominating set if every edge in E − F is adjacent to some e... more A set F of a graph G(V, E) is an edge dominating set if every edge in E − F is adjacent to some edge in F. An edge domination number γ ′ (G) of G is the minimum cardinality of an edge dominating set. An edge dominating set F is called a cototal edge dominating set if the induced subgraph 〈E − F〉 doesnot contain isolated edge. The minimum cardinality of the cototal edge dominating set in G is its domination number and is denoted by γ ′ cot(G). We investigate several properties of cototal edge dominating sets and give some bounds on the cototal edge domination number.
The pathos vertex semientire block graph denoted by P vb (G) is the graph whose vertex set is V(T... more The pathos vertex semientire block graph denoted by P vb (G) is the graph whose vertex set is V(T) b i r and the two vertices are adjacent if and only if they are adjacent vertices, vertices lie on the blocks, vertices lie on the regions and the adjacent blocks. We study the characterization of graphs whose pathos vertex semientire block graph is planar, outer planar, Eulerian and Hamiltonian
International Journal of Computer Applications, 2014
In this communications, the edge semientire block graph of a graph is introduced. We present a ch... more In this communications, the edge semientire block graph of a graph is introduced. We present a characterization of those graphs whose edge semientire block graph is planar, outer planar, Eulerian, Hamiltonian with crossing number one.
International Journal of Computer Applications, 2014
A set S ⊆ V (G) is a split geodetic set of G, if S is a geodetic set and V − S is disconnected. T... more A set S ⊆ V (G) is a split geodetic set of G, if S is a geodetic set and V − S is disconnected. The split geodetic number of a graph G, is denoted by g s (G), is the minimum cardinality of a split geodetic set of G. A set S ⊆ V (G) is a strong split geodetic set of G, if S is a geodetic set and V − S is totally disconnected. The strong split geodetic number of a graph G, is denoted by g ss (G), is the minimum cardinality of a strong split geodetic set of G. In this paper we obtain the geodetic number, split geodetic number, strong split geodetic number and non split geodetic number of strong product graphs, composition of graphs and join of graphs.
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Papers by Venkanagouda Goudar