Abstract
If G=(VG,EG) is a graph of order n, we call S⊆VG an isolating set if the graph induced by VG−NG[S] contains no edges. The minimum cardinality of an isolating set of G is called the isolation number of G, and it is denoted by ι(G). It is known that ι(G)≤n3 and the bound is sharp. A subset S⊆VG is called dominating in G if NG[S]=VG. The minimum cardinality of a dominating set of G is the domination number, and it is denoted by γ(G). In this paper, we analyze a family of trees T where ι(T)=γ(T), and we prove that ι(T)=n3 implies ι(T)=γ(T). Moreover, we give different equivalent characterizations of such graphs and we propose simple algorithms to build these trees from the connections of stars.
Funder
Xunta de Galicia
Agencia Estatal de Investigación of Spain
Subject
General Mathematics,Engineering (miscellaneous),Computer Science (miscellaneous)
Cited by
1 articles.
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