Some Nordhaus - Gaddum Type Relations On Strong Efficient Dominating Sets

Authors : K MURUGAN, N MEENA

Pages : 4-16

View : 53 | Download : 10

Publication Date : 2016-08-08

Article Type : Research Paper

Abstract :Let G = insert ignore into journalissuearticles values(V, E); be a simple graph with p vertices and q edges. A subset S of Vinsert ignore into journalissuearticles values(G); is called a strong insert ignore into journalissuearticles values(weak); efficient dominating set of G if for every vVinsert ignore into journalissuearticles values(G);,│Ns[v]∩S│=1insert ignore into journalissuearticles values(│Nw[v]∩S│=1);.Nsinsert ignore into journalissuearticles values(v); ={u Vinsert ignore into journalissuearticles values(G); uv Einsert ignore into journalissuearticles values(G);, deginsert ignore into journalissuearticles values(u); ≥ deginsert ignore into journalissuearticles values(v);}.The minimum cardinality of a strong insert ignore into journalissuearticles values(weak); efficient dominating set G is called strong insert ignore into journalissuearticles values(weak); efficient domination number of G and is denoted by γse insert ignore into journalissuearticles values(γwe );. A graph G is strong efficient if there exists a strong efficient dominating set of G. In this paper, the authors introduced a new parameter called the number of strong efficient dominating sets of a graph G denoted by # γse insert ignore into journalissuearticles values(G); and studied some Nordhaus- Gaddum type relations on strong efficient domination number of a graph and its derived graph. The relation between the number of strong efficient dominating sets of a graph and its derived graph is also studied
Keywords : Strong efficient dominating sets, Strong efficient domination number and number of strong efficient dominating sets

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