The expected values of Kirchhoff indices in the random polyphenyl and spiro chains - Huang, Guihua (Ars mathematica contemporanea, 2015)
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: average value; expected value; Kirchhoff index; Kirchhoffov indeks; matematično upanje (pričakovana vrednost); polifenilna veriga; polyphenyl chain; povprečna vrednost; resistance distance; rezistenčna razdalja; spiro chain; spiro veriga