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Total well dominated trees

By Arthur Finbow, Allan Frendrup and Preben D. Vestergaard

Abstract

Let G = (V,E) be a graph with no isolated vertex. A set D is called total dominating in G if each vertex in G is adjacent to a vertex from D, and D is a minimal total dominating set if any subset D′ ⊂ D is not a total dominating set in G. If all minimal total dominating sets in G have the same cardinality then G is a total well dominated graph. In this paper we study composition and decomposition of total well dominated trees. By a reversible process we prove that any total well dominated tree can both be reduced to and constructed from a family of three small trees.Let G = (V,E) be a graph with no isolated vertex. A set D is called total dominating in G if each vertex in G is adjacent to a vertex from D, and D is a minimal total dominating set if any subset D′ ⊂ D is not a total dominating set in G. If all minimal total dominating sets in G have the same cardinality then G is a total well dominated graph. In this paper we study composition and decomposition of total well dominated trees. By a reversible process we prove that any total well dominated tree can both be reduced to and constructed from a family of three small trees

Publisher: Department of Mathematical Sciences, Aalborg University
Year: 2009
OAI identifier: oai:pure.atira.dk:publications/79f8e960-909b-11de-90ca-000ea68e967b
Provided by: VBN

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