Generalized adjacency and Laplacian spectra of the weighted corona graphs

Abstract

Recently, corona product graphs have attracted a great deal of attention from scientific communities, such as coding theory, frequency assignment, mathematical chemistry. Meanwhile, weight factor gradually became a research hotpoint because of closing to reality. Hence, we introduce the weighted corona graphs in this paper. The weighted corona product graphs are the in-depth and promotion of the corona product graphs, linking the spectra between the initial graph and the product graph. Then, we deduce the complete information of generalized adjacency and Laplacian eigenvalues of the weighted product graph with different structures. And we generalize the results obtained previously into product corona graph with m(⩾1) iterations.