Abstract
ABSTRACTLet G be a connected graph. The quadrilateral graph of G, denoted by is the graph obtained from G by replacing each edge in G with two parallel paths of lengths 1 and 3. In this paper, the complete information for the eigenvalues of the probability transition matrix of a random walk on in terms of those of G is provided. Then the expected hitting time between any two vertices of in terms of those of G is completely determined. Finally, as applications, the correlation between the degree-Kirchhoff index (resp. Kemeny’s constant, number of spanning trees) of and G is derived. Furthermore, based on the relationship of the expected hitting time between any two vertices of and G, the resistance distance between any two vertices of is presented in terms of that of G.
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