Domination versus independent domination in cubic graphs
نویسندگان
چکیده
منابع مشابه
Independent Domination in Cubic Graphs
A set S of vertices in a graph G is an independent dominating set of G if S is an independent set and every vertex not in S is adjacent to a vertex in S. The independent domination number of G, denoted by i(G), is the minimum cardinality of an independent dominating set. In this paper, we show that if G �= C5 ✷K2 is a connected cubic graph of order n that does not have a subgraph isomorphic to ...
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Let v(G) and γ(G) denote the number of vertices and the domination number of a graph G, respectively, and let ρ(G) = γ(G)/v(G). In 1996 B. Reed conjectured that if G is a cubic graph, then γ(G) ≤ dv(G)/3e. In 2005 A. Kostochka and B. Stodolsky disproved this conjecture for cubic graphs of connectivity one and maintained that the conjecture may still be true for cubic 2-connected graphs. Their m...
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The domination number γ(G) and the total domination number γt(G) of a graph G without an isolated vertex are among the most well studied parameters in graph theory. While the inequality γt(G) ≤ 2γ(G) is an almost immediate consequence of the definition, the extremal graphs for this inequality are not well understood. Furthermore, even very strong additional assumptions do not allow to improve t...
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ژورنال
عنوان ژورنال: Discrete Mathematics
سال: 2013
ISSN: 0012-365X
DOI: 10.1016/j.disc.2012.01.003