Abstract
In this paper, we introduce the generalized quadrilateral graph Q (n) (G), which can be got by replacing each edge of the given graph G with a complete bipartite graph K n,n . We characterize all the spectrum of the graph Q (n) (G) in terms of the given graph. Then we derive the formula for the multiplicative degree-Kirchhoff index, the Kemeny’s constant and the number of spanning trees of Q (n) (G). Finally, we can obtain more about the iterative graph Q r (n) (G).
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