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

Access to Document

10.7151/dmgt.2222

Cite this

@article{9da072e536454af68c85d31d3650e06f,

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) \ 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.",

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",

month = may,

day = "1",

doi = "10.7151/dmgt.2222",

language = "English",

volume = "41",

pages = "633--645",

journal = "Discussiones Mathematicae - Graph Theory",

issn = "1234-3099",

publisher = "University of Zielona Gora",

number = "2",

}

TY - JOUR

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 - http://www.scopus.com/inward/record.url?scp=85068787128&partnerID=8YFLogxK

U2 - 10.7151/dmgt.2222

DO - 10.7151/dmgt.2222

M3 - Article

AN - SCOPUS:85068787128

SN - 1234-3099

VL - 41

SP - 633

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

Access to Document

Other files and links

Fingerprint

Cite this