科研之友
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摘要
Let F-q be a finite field of order q and let R be a finite commutative local ring which is not a field. Recently, three (resp. four) distinct eigenvalues of the unitary Cayley graph C-Mn(Fq) (resp. C-Mn(R)) have been determined in Rattanakangwanwong and Meemark (2020) [20]. In this paper, completely explicit closed formulas for all the eigenvalues of C-Mn(Fq) and C-Mn(R) are obtained by using a new approach. As applications, the energy, the Kirchhoff index and the number of spanning trees of C-Mn(Fq) and C-Mn(R) are derived, respectively.
