Two Kinds of Laplacian Spectra and Degree Kirchhoff Index of the Weighted Corona Networks. (10th February 2022) - Liu, Haiqin; Shao, Yanling
Abstract : Recently, the study related to network has aroused wide attention of the scientific community. Many problems can be usefully represented by corona graphs or networks. Meanwhile, the weight is a vital factor in characterizing some properties of real networks. In this paper, we give complete information about the signless Laplacian spectra of the weighted corona of a graph G 1 and a regular graph G 2 and the complete information about the normalized Laplacian spectra of the weighted corona of two regular graphs. The corresponding linearly independent eigenvectors of all these eigenvalues are also obtained. The spanning trees' total number and the degree Kirchhoff index of the weighted corona graph are computed.