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期刊论文

A Simple Method for Computing Resistance Distance

肖文俊Ravindra B. Bapat Ivan Gutman ab and Wenjun Xiao b

Z. Naturforsch. 58a, 494-498 (2003); received August 2, 2003,-0001,():

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摘要/描述

The resistance distance ri j between two vertices vi and vj of a (connected, molecular) graph G is equal to the effective resistance between the respective two points of an electrical network, constructed so as to correspond to G, such that the resistance of any edge is unity. We show how ri j can be computed from the Laplacian matrix L of the graph G: Let L(i) and L(i, j) be obtained from L by deleting its i-th row and column, and by deleting its i-th and j-th rows and columns, respectively. Then ri j=detL(i, j)/detL(i).

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