Spectral properties of the cartesian product of K_m \square K_g graph
Abstract
This paper investigates the Laplacian spectral properties of the Cartesian product of graph Km□Kg, focusing on the trace, energy, and characteristic polynomial coefficients of Laplacian matrix of the graph. 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 for Km□Kg graph, also found upper bounds of eigenvalue of Laplacian matrix of Km□Kg.
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