On spectra of square edge-corona graphs

Given two connected graphs, G and H. The Order and size of Gand H, are u and v, and m and n, respectively. Graph G square edge-corona H , denoted by G ⋄ 2 H and defined as G ⋄ 2 H : = ( G ⋄ H ) ⋄ H , that is a graph obtained from G, the first v -copies of H that is H h , with h ∈ {1,2,…, v ], and the second v (1 + 2n + m )-copies of H that is H hk , with h ∈ {1,2,…, v ] and k ∈ {1,2,…,1 + 2 n + m ] and joining the terminal vertices of e h ∈ E ( G ), with e h = i h j h and i h , j h ∈ V ( G ), to all vertices of H h , and then joining the terminal vertices of e k = r k s k , e k ∈ G ⋄ H, to all vertices of H hk . In this paper, the spectrum of the adjacency, Laplacian, and signless-Laplacian matrices of the graph G ⋄ 2 H will be analyzed further.