INVERSE DOMINATION NUMBER OF JUMP GRAPH

M Karthikeyan,A Elumalai

doi:10.12732/ijpam.v103i3.9

M Karthikeyan, A Elumalai

Open Access

https://doi.org/10.12732/ijpam.v103i3.9

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Abstract

Let J(G) = (V,E) be a jump graph. Let D be a minimum dominating set in a jump Graph J(G). If V − D contains a dominating set Dof J(G), then Dis called an inverse dominating set with respect to D. The minimum cardinality of an inverse dominating set of a Jump graph J(G) is called the inverse domination number of J(G). In this paper We study the graph theoretic properties of inverse domination of Jump graph and its exact values for some standard graphs. The relation between inverse domination of Jump graph with other parameters is also investigated.

Highlights

Let G(p, q) be a graph with p = |V | and q = |E| denote the number of vertices and edges of a graph G respectively
The minimum cardinality of an inverse dominating set of a jump graph J(G) is called the inverse domination number of J(G) and it is denoted by γ−1[J(G)]
Since we study only the connected jump graph, we choose p > 4 [5]

Summary

Introduction

Let G(p, q) be a graph with p = |V | and q = |E| denote the number of vertices and edges of a graph G respectively. A set D of vertices in a graph G = (V, E) is a dominating set if every vertex in V − D is adjacent to some vertex in D. Let D be a minimum dominating set of G. The maximum (minimum) degree among the vertices of G is denoted by ∆(G) (δ(G)).

Results

Conclusion