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Keywords:
DS (determined by spectrum) graph; Schläfli graph; multicone graph; adjacency spectrum; Laplacian spectrum; Paley graph of order 17
DS (determined by spectrum) graph; Schläfli graph; multicone graph; adjacency spectrum; Laplacian spectrum; Paley graph of order 17
Summary:
Finding and discovering any class of graphs which are determined by their spectra is always an important and interesting problem in the spectral graph theory. The main aim of this study is to characterize two classes of multicone graphs which are determined by both their adjacency and Laplacian spectra. A multicone graph is defined to be the join of a clique and a regular graph. Let $ K_w $ denote a complete graph on $ w $ vertices, and let $ m $ be a positive integer number. In A. Z. Abdian (2016) it has been shown that multicone graphs $ K_w\bigtriangledown P_{17}$ and $ K_w\bigtriangledown S$ are determined by both their adjacency and Laplacian spectra, where $ P_{17} $ and $ S$ denote the Paley graph of order 17 and the Schläfli graph, respectively. In this paper, we generalize these results and we prove that multicone graphs $ K_w\bigtriangledown mP_{17}$ and $ K_w\bigtriangledown mS$ are determined by their adjacency spectra as well as their Laplacian spectra.
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