The Spectral Determinations of the Multicone Graphs $ K_w\bigtriangledown P_{17}\bigtriangledown P_{17} $ and $ K_w\bigtriangledown S\bigtriangledown S$

Authors : Maryam RAHMANİ MOGHADDAM, Kewen ZHAO, Sara POUYANDEH, Ali ZEYDİ ABDİAN

Pages : 192-198

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Publication Date : 2019-04-15

Article Type : Research Paper

Abstract :Characterizing classes of graphs which are determined by their spectra is often a hard and challenging problem. So, finding and introducing any class of these graphs can be an interesting and important problem. This paper aims to characterize new classes of multicone graphs which are determined by both their adjacency spectra and their Laplacian spectra. A multicone graph is obtained from the join of a clique and a regular graph. Let $ K_w $ be a complete graph on $ w $ vertices. It is proved that multicone graphs $ K_w\bigtriangledown P_{17}\bigtriangledown P_{17}$ and $ K_w\bigtriangledown S\bigtriangledown S$ are determined by both their adjacency spectra and their Laplacian spectra, where $ P_{17} $ and $S$ denote Paley graph of order 17 and Schlafli graph, respectively.
Keywords : Adjacency spectrum, Laplacian spectrum, Multicone graph, Paley graph of order 17, DS graph, Schlafli graph