A NOTE ON THE EIGENVALUES OF n-CAYLEY GRAPHS

Authors

  • M. Arezoomand University of Larestan, Larestan, 74317-16137, Iran Author

Keywords:

Semi-Cayley graph, n-Cayley graph, quasi-abelian, eigenvalue

Subjects:

05C50, 05C25, 05C31

Abstract

A graph Γ is called an n-Cayley graph over a group G if its automorphism containsa semi-regular subgroup isomorphic to G with n orbits. Every n-Cayley graph over a group G is completely determined byn2 suitable subsets of G. If each of these subsets is a union of conjugacy classes of G, then it is called a quasi-abelian n-Cayleygraph over G. In this paper, we determine the characteristic polynomial of quasi-abelian n-Cayley graphs. Then we exactly determine theeigenvalues and the number of closed walks of quasi-abelian semi-Cayley graphs. Furthermore, we construct some integral graphs.

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Published

2020-10-15