# DMGT

ISSN 1234-3099 (print version)

ISSN 2083-5892 (electronic version)

# IMPACT FACTOR 2019: 0.755

SCImago Journal Rank (SJR) 2019: 0.600

Rejection Rate (2018-2019): c. 84%

# Discussiones Mathematicae Graph Theory

Article in press

Authors:

W.J. Desormeaux, T.W. Haynes and M.A. Henning

Title:

Restrained domination in self-complementary graphs

Source:

Discussiones Mathematicae Graph Theory

Received: 2018-05-08, Revised: 2019-03-23, Accepted: 2019-03-23, https://doi.org/10.7151/dmgt.2222

Abstract:

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 $V(G) \setminus S$ is adjacent to a vertex in $S$ and to a vertex in $V(G) \setminus S$. 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.

Keywords:

domination, complement, restrained domination, self-complementary graph