Research Article

Convex Hull of γvct-sets in Graphs

by  R.Vasanthi, K.Subramanian
journal cover
International Journal of Computer Applications
Foundation of Computer Science (FCS), NY, USA
Volume 180 - Issue 23
Published: Feb 2018
Authors: R.Vasanthi, K.Subramanian
10.5120/ijca2018915932
PDF

R.Vasanthi, K.Subramanian . Convex Hull of γvct-sets in Graphs. International Journal of Computer Applications. 180, 23 (Feb 2018), 1-4. DOI=10.5120/ijca2018915932

                        @article{ 10.5120/ijca2018915932,
                        author  = { R.Vasanthi,K.Subramanian },
                        title   = { Convex Hull of γvct-sets in Graphs },
                        journal = { International Journal of Computer Applications },
                        year    = { 2018 },
                        volume  = { 180 },
                        number  = { 23 },
                        pages   = { 1-4 },
                        doi     = { 10.5120/ijca2018915932 },
                        publisher = { Foundation of Computer Science (FCS), NY, USA }
                        }
                        %0 Journal Article
                        %D 2018
                        %A R.Vasanthi
                        %A K.Subramanian
                        %T Convex Hull of γvct-sets in Graphs%T 
                        %J International Journal of Computer Applications
                        %V 180
                        %N 23
                        %P 1-4
                        %R 10.5120/ijca2018915932
                        %I Foundation of Computer Science (FCS), NY, USA
Abstract

Let G = (V, E) be an undirected, simple and connnected graph. A set C ⊆ V of vertices in G is called a convex set if I(C) = C where I(C) is the set of all vertices in the u-v geodesic path of G for all u, v ∈ C. For any set C ⊆ V, the convex hull of C denoted by [C] is defined as the smallest convex subset of V(G) containing C. Let S be a minimum vertex covering transversal dominating set viz. a γvct-set. Then the convex hull of S is defined as the smallest convex set containing S. We define the convex hull number of G with respect to γvct-sets, denoted by CHγvct(G) as CH γvct(G) = min.{|C|: C = [S] is the convex hull of γvct-set S} where the minimum is taken over all the vct-sets of G. If [S] = S, then S is called a convex γvct-set. If [S] = V(G), then S is called a hull γvct-set. In this paper, the convex hull of γvct-sets and the convex hull number with respect to γvct-sets in various graphs are analysed.

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Index Terms
Computer Science
Information Sciences
No index terms available.
Keywords

minimum vertex covering transversal dominating set convex hull number of G with respect to vct-sets convex vct-set hull vct- set

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