Semitotal domination in graphs

Authors

  • Goddard, Wayne
  • Henning, Michael A.
  • McPillan, Charles A

Abstract

In this paper we introduce a parameter that is squeezed between arguably the two most important domination parameters, namely the domination number and the total domination number. We define a set S of vertices in a graph G with no isolated vertices to be a semitotal dominating set of G if it is a dominating set of G and every vertex in S is within distance 2 of another vertex of S. The semitotal domination number, denoted by γt2(G), is the minimum cardinality of a semitotal dominating set of G. We show that if G is a connected graph on n > 4 vertices, then γt2(G) < n/2y and we characterize the trees and graphs of minimum degree 2 achieving this bound.

Published

2014-06-09

How to Cite

Goddard, Wayne, Henning, Michael A., & McPillan, Charles A. (2014). Semitotal domination in graphs. Utilitas Mathematica, 94. Retrieved from https://utilitasmathematica.com/index.php/Index/article/view/1092

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