2023/11/17 by Xiaxia Zhang, Zhang, Xiaxia, Xiaoling Ma +1
Mathematics · Engineering · Computer Science · #Graph theory and applications #graph theory and CDMA systems #Matrix Theory and Algorithms
paper · pdf · doi:10.48550/arxiv.2311.10545
Let G, Hi be simple graphs with n=|V(G)|, m=|E(G)| and i=1, 2, …, n(m). The generalized corona, denoted Go\wedgeni=1 Hi, is the graph obtained by taking one copy of graphs G, H1,…, Hn and joining the ith vertex of G to every vertex of Hi for 1 ≤ i ≤ n. The generalized edge corona, denoted by G[Hi]1m, is the graph obtained by taking one copy of graphs G, H1,…, Hm and then joining two end-vertices of the ith edge of G to every vertex of Hi for 1 ≤ i ≤ m. For any real α∈[0,1], the matrix Aα(G)=αD(G)+(1-α)A(G), where A(G) and D(G) are the adjacency matrix and the degree matrix of a graph G, respectively. In this paper, we obtain the Aα-characteristic polynomial of Go\wedgeni=1 Hi, which extends some known results. Meanwhile, we determine the Aα-characteristic polynomial of G[Hi]1m and get the Aα-spectrum of G[Hi]1m when G and Hi are regular graphs for 1≤ i≤ m. As an application of the above conclusions, we construct infinitely many pairs of non-regular Aα-cospectral graphs.