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Graph Cyclicity, Excess Conductance, and Resistance Deficit

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Abstract

A new graph-theoretic cyclicity index C(G) is defined, being motivated in terms of mathematical concepts from the theory of electrical networks. This “global bond excess conductance” index C(G) then is investigated, with a number of theorems as well as some discussion and numerical investigation. It is found that C(G) typically has less degeneracy than the standard cyclomatic number and has some intuitively appealing features.

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Authors and Affiliations

  1. Texas A&M University at Galveston, Galveston, TX, 77553-1675, USA

    D.J. Klein

  2. Human Biological Chemistry & Genetics, University of Texas Medical Branch, Galveston, TX, 77555, USA

    O. Ivanciuc

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  1. D.J. Klein
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  2. O. Ivanciuc
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Klein, D., Ivanciuc, O. Graph Cyclicity, Excess Conductance, and Resistance Deficit. Journal of Mathematical Chemistry 30, 271–287 (2001). https://doi.org/10.1023/A:1015119609980

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