BOUNDS IN STRONG ROMAN DOMINATION

K. Selvakumar, Dr. M. Kamaraj

Abstract

This article presents sharp lower and upper bounds for γ_R(G) in term of diam (G). Recall that the eccentricity of vertex v in ecc (v) = max{d(u,w):w∈V} and the diameter of G is diam (G) = max{ ecc (v): v∈V}. It has been assumed throughout this article that G is a nontrivial graph of order n≥ 2. ‘Bounds on Roman domination number of a graph G containing cycles, in terms of its girth’ has been presented. Recall that the girth of G (denoted by g(G)) is the length of the smallest cycle in G. Assume throughout this article that G is a non-trivial graph of order n ≥ 3 and contains a cycle.

Keywords:

:Roman domination, Strong Roman domination, Bounds.


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References


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