[Objective]Important structural and dynamical properties of networks can be obtained from the eigenvalues and eigenvectors of matrices associated with their graph representations.Spectra of a graph present information on the diameter,degree distribution,paths of a given length,number of spanning trees and many more invariants.[Methods]In this paper,we present a new graph operation called the edge total corona G1⊙G2 on G1 and G2 involving the total graph of G1,where G1 and G2 denote two simple connected graphs.[Results]The adjacency(respectively,Laplacian and signless Laplacian)spectra of G1 ⊙G2 are obtained in terms of these of a regular graph G1 and an arbitrary graph G2.[Conclusion]As applications of above-mentioned results,we construct initially many pairs of adjacency(respectively,Laplacian and signless Laplacian)cospectral graphs.Furthermore,we also compute the Kirchhoff index and the number of spanning trees of G1⊙G2
edge total corona graphadjacency spectraLaplacian spectrasignless Laplacian spectraKirchhoff indexspanning tree
万方数据
维普
