Discussiones Mathematicae Graph Theory (May 2021)

Restrained Domination in Self-Complementary Graphs

  • Desormeaux Wyatt J.,
  • Haynes Teresa W.,
  • Henning Michael A.

DOI
https://doi.org/10.7151/dmgt.2222
Journal volume & issue
Vol. 41, no. 2
pp. 633 – 645

Abstract

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A self-complementary graph is a graph isomorphic to its complement. A set S of vertices in a graph G is a restrained dominating set if every vertex in V(G) \ S is adjacent to a vertex in S and to a vertex in V(G) \ S. The restrained domination number of a graph G is the minimum cardinality of a restrained dominating set of G. In this paper, we study restrained domination in self-complementary graphs. In particular, we characterize the self-complementary graphs having equal domination and restrained domination numbers.

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