The spectral determination of the connected multicone graphs

AKCE International Journal of Graphs and Combinatorics

Ali Zeydi Abdian¹  Lowell W. Beineke²  Reza Tayebi Khorami³  Mohammad Reza Oboudi⁴  Krishnaiyan Thulasiraman⁵ 

[1] College of Science, Lorestan University;Department of Mathematical Sciences, Purdue University Fort Wayne;Department of Mathematics, Ahvaz Branch, Islamic Azad University;Department of Mathematics, College of Sciences, Shiraz University;School of Computer Science, University of Oklahoma;

关键词: adjacency spectrum;    laplacian spectrum;    ds graph;    multicone graph;    wheel graph;   

DOI  :  10.1080/09728600.2021.1917974

来源: DOAJ

【 摘 要 】

The main goal of the paper is to answer an unsolved problem. A multicone graph is defined to be the join of a clique and a regular graph, and a wheel as the join of a vertex and a cycle. In this study, we present new classes of multicone graphs that are natural generalizations of wheel graphs and we show that they are determined by their adjacency spectra as well as their Laplacian spectra. We also show that the complements of some of these graphs are determined by their adjacency spectra. In addition, we give a necessary and sufficient condition for perfect graphs cospectral with some of the graphs investigated in the paper. Finally, we conclude with two problems for further study.

【 授权许可】

Unknown