The Product Distance Matrix of a Tree and a Bivariate Zeta Function of a Graph∗
نویسندگان
چکیده
We define the product distance matrix of a tree and obtain formulas for its determinant and inverse. The results generalize known formulas for the exponential distance matrix. When we restrict the number of variables to two, we are naturally led to define a bivariate analogue of the laplacian matrix of an arbitrary graph. We also define a bivariate analogue of the Ihara-Selberg zeta function and show its connection with the bivariate laplacian. Finally, for connected graphs we prove an analogue of a result of Northshield connecting a partial derivative of the determinant of the bivariate laplacian and its number of spanning trees.
منابع مشابه
Ela the Product Distance Matrix of a Tree and a Bivariate Zeta Function of a Graph
In this paper, the product distance matrix of a tree is defined and formulas for its determinant and inverse are obtained. The results generalize known formulas for the exponential distance matrix. When the number of variables are restricted to two, the bivariate analogue of the laplacian matrix of an arbitrary graph is defined. Also defined in this paper is a bivariate analogue of the Ihara-Se...
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