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Results on Total Restrained Domination in Graphs

Nader Jafari Rad

Open publisher page 4 citations

Abstract

Let G =(V,E) be a graph. A set S ⊆ V (G) is a total restrained dominating set if every vertex of G is adjacent to a vertex in S and every vertex of V (G)\\S is adjacent to a vertex in V (G)\\S. The total restrained domination number of G, denoted by γtr(G), is the smallest cardinality of a total restrained dominating set of G. In this paper we continue the study of total restrained domination in graphs and obtain some new results.

About this research paper

What this paper is about

Let G =(V,E) be a graph. A set S ⊆ V (G) is a total restrained dominating set if every vertex of G is adjacent to a vertex in S and every vertex of V (G)\\S is adjacent to a vertex in V (G)\\S. The total restrained domination number of G, denoted by γtr(G), is the smallest cardinality of a total restrained dominating set of G. In this paper we continue the study of total restrained domination in graphs and obtain some new results.

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OpenAlex reports 4 citations for this work. Citation counts describe recorded attention and do not establish research quality.

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Available abstract

Let G =(V,E) be a graph. A set S ⊆ V (G) is a total restrained dominating set if every vertex of G is adjacent to a vertex in S and every vertex of V (G)\\S is adjacent to a vertex in V (G)\\S. The total restrained domination number of G, denoted by γtr(G), is the smallest cardinality of a total restrained dominating set of G. In this paper we continue the study of total restrained domination in graphs and obtain some new results.

Key concepts: Dominating set, Combinatorics, Vertex (graph theory), Domination analysis, Mathematics, Graph, Discrete mathematics

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