ARTICLE NAME:

SOME NEW PARAMETERS ON STRONG EFFICIENT DOMINATION

AUTHOR NAME

K.Murugan

ISSUE:

VOL.1, NO.2

YEAR:

2018

PAGE NO:

154-172

ABSTRACT:

Let G = (V, E) be a simple graph with p vertices and q edges. A subset S of V is called a strong (weak) efficient dominating set of G if for every v  V , │Ns[v]∩S│ = 1 (│Nw[v]∩S│= 1). Ns(v) = { u V(G) : uv E(G), deg(u) ≥ deg(v) }.The minimum cardinality of a strong (weak) efficient dominating set of G is called strong (weak) efficient domination number of G and is denoted by γse (γwe ). A graph G is strong efficient if there exists a strong efficient dominating set of G. In this paper, Subdivision number, Anti subdivision number and Subdivision stability number of a strong efficient graph are introduced. Subdivision deficiency number of a non strong efficient graph is also introduced.

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