The expected values of Kirchhoff indices in the random polyphenyl and spiro chains

Guihua Huang, Meijun Kuang, Hanyuan Deng

Abstract


The Kirchhoff index Kf(G) of a graph G is the sum of resistance distances between all pairs of vertices in G. In this paper, we obtain exact formulas for the expected values of the Kirchhoff indices of the random polyphenyl and spiro chains, which are graphs of a class of unbranched multispiro molecules and polycyclic aromatic hydrocarbons. Moreover, we obtain a relation between the expected values of the Kirchhoff indices of a random polyphenyl and its random hexagonal squeeze, and the average values for the Kirchhoff indices of all polyphenyl chains and all spiro chains with n hexagons, respectively.

Keywords


Expected value, average value, Kirchhoff index, resistance distance, polyphenyl chain, spiro chain.

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DOI: https://doi.org/10.26493/1855-3974.458.7b0

ISSN: 1855-3974

Issues from Vol 6, No 1 onward are partially supported by the Slovenian Research Agency from the Call for co-financing of scientific periodical publications