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...

Let Wn = K1 ∨ Cn−1 be the wheel graph on n vertices, and let S(n, c, k) be the graph on n vertices obtained by attaching n− 2c− 2k − 1 pendant edges together with k hanging paths of length two at vertex v0, where v0 is the unique common vertex of c triangles. In this paper we show that S(n, c, k) (c > 1, k > 1) and Wn are determined by their signless Laplacian spectra, respectively. Moreover, w...