The lollipop graph is determined by its spectrum

Details The lollipop graph is determined by its spectrum The lollipop graph is determined by its spectrum

2008-02-07

arxiv.org/abs/0802.1035v1

Mathematics

General Mathematics

Scientific paper

An even (resp. odd) lollipop is the coalescence of a cycle of even (resp. odd) length and a path with pendant vertex as distinguished vertex. It is known that the odd lollipop is determined by its spectrum and the question is asked by W. Haemers, X. Liu and Y. Zhang for the even lollipop. We revisit the proof for odd lollipop, generalize it for even lollipop and therefore answer the question. Our proof is essentially based on a method of counting closed walks.

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