Spectra of four new Graphs join based on Subdivision and Central Graph

Abstract

We define four new graphs through the join operation of subdivision graph S(G) and central graph C(H), namely subdivision vertex-central vertex join S(G)C(H), subdivision edge-central edge join S(G)C(H), subdivision edge-central vertex join S(G)C(H), and subdivision vertex-central edge join S(G)C(H) graphs. We determine the adjacency and Laplacian spectra of these four graphs and generate a set of A-cospectral and L-cospectral non-regular graphs for these new graphs by choosing two pairs of regular cospectral graphs. Additionally, we compute the Kirchhoff indices and the number of spanning trees in these graphs.