A Note on Laplacian Spectrum of Complementary Prisms

Authors : Hande TUNÇEL GÖLPEK

Pages : 72-80

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Publication Date : 2019-12-30

Article Type : Conference Paper

Abstract :In this work, the Laplacian spectrum of Complementary Prism graph is considered. The complementary prism operation was introduced by Haynes et al. and denoted by $G\bar{G}$. Some upper and lower bounds obtained using majorization and operator definition of Laplacian. Beside Cardoso et al.`s results in literature about Laplacian spectrum of complementary prisms, an alternative proof about nonzero minimum and maximum Laplacian eigenvalue of complementary prism that contains disconnected components in the underlying graph $G$ or  $\bar{G}$ is provided. Also using this result, the lower and upper bound of nonzero minimum and maximum Laplacian eigenvalue of the complementary prism graph is emphasized.
Keywords : Laplacian Matrix, Eigenvalues, Complementary Prisms