Resistance-Distance Sum Rules*

By Douglas J. Klein. 2002

193 citations recorded by the source corpus.

The chemical potential for a novel intrinsic graph metric, the resistance distance, is briefly recalled, and then a number of » sum rules« for this metric are established. »Global« and » local « types of sum rules are identified. The sums in the » global « sum rules are graph invariants, and the sum rules provide inter-relations amongst different invariants, some involving the resistance distance while others do not. Illustrative applications to more » regular « graphs are made.

View Paper: https://www.semanticscholar.org/paper/dcd885fe401f84ade93bb1b5fcd4be13096fd37b

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Citations in the corpus

Unicyclic graphs with extremal Kirchhoff index (2008, background): “As an intrinsic graph metric and a relevant tool to characterize wave- or fluid-like communication between two vertices [4], resistance distance is well studied both in mathematical and chemical literatures [5, 6, 7, 8, 9, 10, 11, 12].”
Some results on resistance distances and resistance matrices (2015, background): “3 [5] Let G be a connected graph of order n with edge set E.”
Minimizing Effective Resistance of a Graph (2008, background): “Some papers on various aspects of resistance distance include [Kle02], [XG03], [Bap99], [KR93].”
ON THE NORMALISED LAPLACIAN SPECTRUM, DEGREE-KIRCHHOFF INDEX AND SPANNING TREES OF GRAPHS (2015, unknown): “This new parameter is in fact intrinsic to the graph and has some nice interpretations and applications in chemistry (see [13, 14] for details).”