ARTICLE NAME:

CHARACTERIZING GRAPHS OF ORDER N WHOSE SUM OF STRONG EFFICIENT DOMINATION NUMBER AND CHROMATIC NUMBER IS N + 1

AUTHOR NAME

N.MEENA

ISSUE:

VOL.1, NO.2

YEAR:

2018

PAGE NO:

173-184

ABSTRACT:

Let G = (V,E) be a graph. A subset S of V(G) is called a strong (weak) efficient dominating set of G if for every v  V(G), │Ns[v]∩S│ = 1 (│Nw[v]∩S│ = 1), where Ns(v) = {u V(G): uv E(G), deg u ≥ deg v } and Nw(v) = { u V(G) : uv E(G), deg v ≥ deg u}, Ns[v] = Ns(v) {v}, (Nw[v] = Nw(v) {v}). The minimum cardinality of a strong (weak) efficient dominating set of G is called the strong (weak) efficient domination number of G and is denoted by γse(G) (γwe(G)). Let G be a graph on n vertices. In this paper, graphs for which the sum of strong efficient domination number and chromatic number equal to n+1 are characterized.

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