Some Classes of Simultaneous Cospectral Graphs for Adjacency, Laplacian and Normalized Laplacian Matrices
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Authors: A. DAS AND P. PANIGRAHI
DOI: 10.46793/KgJMat2608.1243D
Abstract:
In this paper we construct several classes of non-regular graphs which are co-spectral with respect to all the three matrices, namely, adjacency, Laplacian and normalized Laplacian, and hence we answer a question asked by S. Butler. We make these constructions starting with two pairs (G1, H1) and (G2, H2) of A-cospectral regular graphs, taking their R-graph ℛ(Gi), ℛ(Hi), i = 1,2, and finally making some kind of partial joins between ℛ(G1) and ℛ(G2); and ℛ(H1) and ℛ(H2). Moreover, we determine the number of spanning trees and the Kirchhoff index of the newly constructed graphs.
Keywords:
Adjacency matrix, Laplacian matrix, normalized Laplacian matrix, R-vertex-vertex join, R-edge-edge join, R-edge-vertex join.
References:
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