Spectral Properties of the Cartesian Product Km × Kg Graph
Abstract
abstract: This paper investigates the Laplacian spectral properties of the Cartesian product graph Km ×
Kg, focusing on the trace, energy, and characteristic polynomial coefficients. We derive general formulas for the
trace of Laplacian matrix powers and provide recursive relations for the Laplacian coefficients of characteristic
polynomial using trace identities. Results for Km × Kg are verified and generalized for arbitrary m & g and
also found upper bounds of eigenvalues of Laplacian matrix of Km × Kg.
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