Product Distance Matrix of a Graph and Squared Distance Matrix of a Tree

نویسندگان

  • R. B. Bapat
  • S. Sivasubramanian
چکیده

Let G be a strongly connected, weighted directed graph. We define a product distance η(i, j) for pairs i, j of vertices and form the corresponding product distance matrix. We obtain a formula for the determinant and the inverse of the product distance matrix. The edge orientation matrix of a directed tree is defined and a formula for its determinant and its inverse, when it exists, is obtained. A formula for the determinant of the (entry-wise) squared distance matrix of a tree is proved.

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تاریخ انتشار 2013