Domination versus independent domination in cubic graphs

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Abstract

A set S of vertices in a graph G is a dominating set if every vertex not in S is adjacent to a vertex in S. If, in addition, S is an independent set, then S is an independent dominating set. The domination number γ(G) of G is the minimum cardinality of a dominating set in G, while the independent domination number i(G) of G is the minimum cardinality of an independent dominating set in G. In this paper we show that if G≠K(3,3) is a connected cubic graph, then i(G)/γ(G)≤4/3. This answers a question posed in Goddard (in press) [6] where the bound of 3/2 is proven. In addition we characterize the graphs achieving this ratio of 4/3. © 2012 Elsevier B.V. All rights reserved.

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Southey, J., & Henning, M. A. (2013). Domination versus independent domination in cubic graphs. Discrete Mathematics, 313(11), 1212–1220. https://doi.org/10.1016/j.disc.2012.01.003

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