Abstract

Let D = (V,A) be a digraph. A subset S of V is called a twin dominating set of D if for every vertex v ? V ? S, there exist vertices u1, u2 ? S ( u1 and u2 may coincide) such that (v, u1) and (u2, v) are arcs in D. The minimum cardinality of a twin dominating set in D is called the twin domination number of D and is denoted by ?*(D). In this paper we present several basic results on these and other related parameters.

Highlights

  • Throughout this paper D = (V, A) is a finite, directed graph with neither loops nor multiple arcs and G = (V, E) is a finite, undirected graph with neither loops nor multiple edges

  • In this paper we present in the second section some results on twin domination and in the third section some results on twin domination in oriented graphs

  • A twin dominating set S of a digraph D is a minimal twin dominating set if and only if for each vertex u ∈ S, there exists v ∈ V such that O[v] ∩ S = {u} or I[v] ∩ S = {u}

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Summary

Introduction

Let S be a minimum twin dominating set of P. Suppose γ∗(T ) = 2 and let S = {u, v} be a twin dominating set of T. A twin dominating set S of a digraph D is a minimal twin dominating set if and only if for each vertex u ∈ S, there exists v ∈ V such that O[v] ∩ S = {u} or I[v] ∩ S = {u}.

Results
Conclusion

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