ABSTRACT
Let πΊ=(π,πΈ) be a simple graph. A subset S of π(πΊ) is called a strong (weak) efficient dominating set of G if for every π£βπ(πΊ),|ππ [π£]β©π|=1.(|ππ€[π£]β©π|=1) , where ππ [π£]={π’βπ(πΊ)βΆπ’π£ βπΈ(πΊ),degπ’ β₯degπ£}. (ππ€[π£]={π’βπ(πΊ)βΆπ’π£ βπΈ(πΊ),degπ£ β₯degπ’ The minimum cardinality of a strong (weak) efficient dominating set of G is called the strong (weak) efficient dominating set of G and is denoted by πΎπ π(πΊ) (πΎπ€π(πΊ)). A graph G is strong efficient if there exists a strong efficient dominating set of G. The strong efficient bondage number ππ π(πΊ) of a non empty graph G is the minimum cardinality among all sets of edges πβπΈ such that πΎπ π(πΊβπ)>πΎπ π(πΊ). In this paper, the strong efficient bondage number of some path related graphs and some special graphs are studied.
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