On a Family of 4-Critical Graphs with Diameter Three
نویسندگان
چکیده
Let γt(G) denote the total domination number of the graph G. G is said to be total domination edge critical, or simply γt-critical, if γt(G+ e) < γt(G) for each edge e ∈ E(G). In this paper we study a family H of 4-critical graphs with diameter three, in which every vertex is a diametrical vertex, and every diametrical pair dominates the graph. We also generalize the self-complementary graphs, and show that these graphs provide a special case of the family H.
منابع مشابه
A Note on Total Domination Critical Graphs
The total domination number of G denoted by γt(G) is the minimum cardinality of a total dominating set of G. A graph G is total domination vertex critical or just γt-critical, if for any vertex v of G that is not adjacent to a vertex of degree one, γt(G − v) < γt(G). If G is γt-critical and γt(G) = k, then G is k-γt-critical. Haynes et al [The diameter of total domination vertex critical graphs...
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عنوان ژورنال:
- Ars Comb.
دوره 105 شماره
صفحات -
تاریخ انتشار 2012