Arbitrarily vertex decomposable suns with few rays

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Abstract

A graph G of order n is called arbitrarily vertex decomposable if for each sequence (n1, ..., nk) of positive integers with n1 + ⋯ + nk = n, there exists a partition (V1, ..., Vk) of the vertex set of G such that Vi induces a connected subgraph of order ni, for all i = 1, ..., k. A sun with r rays is a unicyclic graph obtained by adding r hanging edges to r distinct vertices of a cycle. We characterize all arbitrarily vertex decomposable suns with at most three rays. We also provide a list of all on-line arbitrarily vertex decomposable suns with any number of rays. © 2009.

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Kalinowski, R., Pilśniak, M., Woźniak, M., & Zioło, I. (2009). Arbitrarily vertex decomposable suns with few rays. Discrete Mathematics, 309(11), 3726–3732. https://doi.org/10.1016/j.disc.2008.02.019

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