Restrained Domination in Self-Complementary Graphs

Wyatt J. Desormeaux; Teresa W. Haynes; Michael A. Henning

doi:10.7151/dmgt.2222

Restrained Domination in Self-Complementary Graphs

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

Mathematics and Applied Mathematics

Research output: Contribution to journal › Article › peer-review

2 Citations (Scopus)

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) \ 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.

Original language	English
Pages (from-to)	633-645
Number of pages	13
Journal	Discussiones Mathematicae - Graph Theory
Volume	41
Issue number	2
DOIs	https://doi.org/10.7151/dmgt.2222
Publication status	Published - 1 May 2021

Keywords

complement
domination
restrained domination
self-complementary graph

ASJC Scopus subject areas

Discrete Mathematics and Combinatorics
Applied Mathematics

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10.7151/dmgt.2222

Cite this

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title = "Restrained Domination in Self-Complementary Graphs",

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) \textbackslash{} S is adjacent to a vertex in S and to a vertex in V(G) \textbackslash{} 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 = "complement, domination, restrained domination, self-complementary graph",

author = "Desormeaux, \{Wyatt J.\} and Haynes, \{Teresa W.\} and Henning, \{Michael A.\}",

note = "Publisher Copyright: {\textcopyright} 2021 Wyatt J. Desormeaux et al., published by Sciendo 2021.",

year = "2021",

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T1 - Restrained Domination in Self-Complementary Graphs

AU - Desormeaux, Wyatt J.

AU - Haynes, Teresa W.

AU - Henning, Michael A.

PY - 2021/5/1

Y1 - 2021/5/1

N2 - 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.

AB - 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.

KW - complement

KW - domination

KW - restrained domination

KW - self-complementary graph

UR - https://www.scopus.com/pages/publications/85068787128

U2 - 10.7151/dmgt.2222

DO - 10.7151/dmgt.2222

M3 - Article

AN - SCOPUS:85068787128

SN - 1234-3099

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EP - 645

JO - Discussiones Mathematicae - Graph Theory

JF - Discussiones Mathematicae - Graph Theory

IS - 2

ER -

Restrained Domination in Self-Complementary Graphs

Abstract

Keywords

ASJC Scopus subject areas

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