On the Eigenvalues and Energy of the Seidel and Seidel Laplacian Matrices of Graphs

J. Askari, Kinkar Chandra Das, Yilun Shang and M. Palanivel

Discrete Dynamics in Nature and Society, 2024, vol. 2024, 1-11

Abstract: Let SΓ be a Seidel matrix of a graph Γ of order n and let DΓ=diagn−1−2d1,n−1−2d2,…,n−1−2dn be a diagonal matrix with di denoting the degree of a vertex vi in Γ. The Seidel Laplacian matrix of Γ is defined as SLΓ=DΓ−SΓ. In this paper, we obtain an upper bound, and a lower bound on the Seidel Laplacian Estrada index of graphs. Moreover, we find a relation between Seidel energy and Seidel Laplacian energy of graphs. We establish some lower bounds on the Seidel Laplacian energy in terms of different graph parameters. Finally, we present a relation between Seidel Laplacian Estrada index and Seidel Laplacian energy of graphs.

Date: 2024
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Persistent link: https://EconPapers.repec.org/RePEc:hin:jnddns:8390307

DOI: 10.1155/2024/8390307

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