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On arbitrarily vertex decomposable unicyclic graphs with dominating cycle

Sylwia Cichacz;  Irmina A. Zioło — 2006

Discussiones Mathematicae Graph Theory

A graph G of order n is called arbitrarily vertex decomposable if for each sequence (n₁,...,nₖ) of positive integers such that ∑ i = 1 k n i = n , there exists a partition (V₁,...,Vₖ) of vertex set of G such that for every i ∈ 1,...,k the set V i induces a connected subgraph of G on n i vertices. We consider arbitrarily vertex decomposable unicyclic graphs with dominating cycle. We also characterize all such graphs with at most four hanging vertices such that exactly two of them have a common neighbour.

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