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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Official URL: http://scindeks.nb.rs/article.aspx?artid=0340-6253...

## Abstract

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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ID Code: | 77905 |

Deposited On: | 14 Jan 2012 15:26 |

Last Modified: | 14 Jan 2012 15:26 |

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