On self-complementary cyclic packing of forests.
On arbitrarily vertex decomposable unicyclic graphs with dominating cycle
A graph G of order n is called arbitrarily vertex decomposable if for each sequence (n₁,...,nₖ) of positive integers such that , there exists a partition (V₁,...,Vₖ) of vertex set of G such that for every i ∈ 1,...,k the set induces a connected subgraph of G on 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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