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Abstract

Let G (V, E) be a graph, the set D⊆ V is dominating set if each vertex v∈ V is either in D or is adjacent to a vertex in D and if there is no dominating subset of D, D will minimal dominating of a graph G. The domination number γ(G) is the minimum cardinality of all members of a minimal dominating set of a graph G. If V-D includes dominating set D' of vertices of a graph G then D' is called an inverse dominating set to D such that γ-1(G) is the minimum cardinality of every member of minimal inverse dominating set of G. Throughout this paper, two new parameters of domination number which are called the S-domination number γs(G) and the inverse S-domination number γs-1(G) are introduced such that S-dominating set and inverse S-dominating set are proper sets. Theoretical parts and sides of these definitions are discussed. The results and properties of this definition are tackled, especially the definitions are studied on special graphs for instance cycle, path, complete, complete bipartite, wheel and complement of these graphs additionally for another graph helm, lollipop and Dutch windmill have been tackled.

Keywords

Certain graphs, Complement of certain graphs, Invers S-dominating set, S-dominating set, γs-set

Subject Area

Mathematics

Article Type

Article

First Page

2340

Last Page

2349

Creative Commons License

Creative Commons Attribution 4.0 International License
This work is licensed under a Creative Commons Attribution 4.0 International License.

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