Spectral characterization of new classes of multicone graphs
DOI:
https://doi.org/10.24193/subbmath.2017.3.01Keywords:
Adjacency spectrum, Laplacian spectrum, DS graph.Abstract
This paper deals with graphs that are known as multicone graphs. A multicone graph is a graph obtained from the join of a clique and a regular graph. Let w, l, m be natural numbers and k is a natural number. It is proved that any connected graph cospectral with multicone graph Kw 9 mECP k is determined by its adjacency spectra as well as its Laplacian spectra, where ECP k = K 3k , 3k , ..., 3k . Also, we show that complements of some of these multicone graphs are determined by their adjacency spectra. Moreover, we prove that any connected graph cospectral with these multicone graphs must be perfect. Finally, we pose two problems for further researches.
Mathematics Subject Classification (2010): 05C50.
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