Resistance matrix of a weighted graph

Bapat, R. B. (2004) Resistance matrix of a weighted graph Communications in Mathematical and in Computer Chemistry /MATCH, 50 . pp. 73-82. ISSN 0955-4947

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In contrast to the classical notion of distance as the length of a shortest path between two vertices, the concept of resistance distance, introduced by Klein and Randic, arises naturally from several different considerations and is more amenable, to mathematical treatment. For a connected graph with n vertices, the resistance matrix of the graph is defined to be the n × n matrix with its (i, j)-entry equal to the resistance distance between the i-th and the j-th vertices. We obtain a formula for the inverse and the determinant of the resistance matrix of a weighted graph, thereby generalizing some earlier work, including that of Graham, Pollack, Lova'sz, Xiao and Gutman.

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