Total Domination Versus Domination in Cubic Graphs

Joanna Cyman; Magda Dettlaff; Michael A. Henning; Magdalena Lemańska; Joanna Raczek

doi:10.1007/s00373-017-1865-5

Total Domination Versus Domination in Cubic Graphs

Abstract

A dominating set in a graph G is a set S of vertices of G such that every vertex not in S has a neighbor in S. Further, if every vertex of G has a neighbor in S, then S is a total dominating set of G. The domination number,γ(G), and total domination number, γ_t(G), are the minimum cardinalities of a dominating set and total dominating set, respectively, in G. The upper domination number, \Gamma(G), and the upper total domination number, \Gamma_t(G), are the maximum cardinalities of a minimal dominating set and total dominating set, respectively, in G. It is known that γ_t(G)/γ (G)≤2 and \Gamma_t(G)/ \Gamma(G)≤2 for all graphs G with no isolated vertex. In this paper we characterize the connected cubic graphs G satisfying γ_t(G)/γ (G)=2, and we characterize the connected cubic graphs G satisfying \Gamma_t(G)/ \Gamma(G)=2.

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Authors (5)

Joanna Cyman dr
Magda Dettlaff dr inż.
Michael A. Henning
- University of Johannesburg Department of Pure and Applied Mathematics
Magdalena Lemańska dr inż.
Joanna Raczek dr inż.

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Category:: Articles
Type:: artykuł w czasopiśmie wyróżnionym w JCR
Published in:: GRAPHS AND COMBINATORICS no. 34, pages 261 - 276,
ISSN: 0911-0119
Language:: English
Publication year:: 2018
Bibliographic description:: Cyman J., Dettlaff M., Henning M. A., Lemańska M., Raczek J.: Total Domination Versus Domination in Cubic Graphs// GRAPHS AND COMBINATORICS. -Vol. 34, iss. 1 (2018), s.261-276
DOI:: Digital Object Identifier (open in new tab) 10.1007/s00373-017-1865-5
Verified by:: Gdańsk University of Technology