Given graphs Gand G, we define a graph operation on Gand G,namely the SSG-vertex join of Gand G, denoted by G★ G. Let S(G) be the subdivision graph of G. The SSG-vertex join G★Gis the graph obtained from S(G) and S(...Given graphs Gand G, we define a graph operation on Gand G,namely the SSG-vertex join of Gand G, denoted by G★ G. Let S(G) be the subdivision graph of G. The SSG-vertex join G★Gis the graph obtained from S(G) and S(G) by joining each vertex of Gwith each vertex of G. In this paper, when G(i = 1, 2) is a regular graph, we determine the normalized Laplacian spectrum of G★ G. As applications, we construct many pairs of normalized Laplacian cospectral graphs, the normalized Laplacian energy, and the degree Kirchhoff index of G★G.展开更多
文摘Given graphs Gand G, we define a graph operation on Gand G,namely the SSG-vertex join of Gand G, denoted by G★ G. Let S(G) be the subdivision graph of G. The SSG-vertex join G★Gis the graph obtained from S(G) and S(G) by joining each vertex of Gwith each vertex of G. In this paper, when G(i = 1, 2) is a regular graph, we determine the normalized Laplacian spectrum of G★ G. As applications, we construct many pairs of normalized Laplacian cospectral graphs, the normalized Laplacian energy, and the degree Kirchhoff index of G★G.
