The expected values for the Kirchhoff indices in the random cyclooctatetraene and spiro chains

The Kirchhoff index of a graph is the sum of resistance distances between all pairs of vertices in . In this paper, we obtain exact analytical expressions of the expected values for the Kirchhoff indices of the random cyclooctatetraene and spiro chains with octagons, respectively, which are graphs of a class of polycyclic hydrocarbons and unbranched multispiro molecules. We also discuss the average values for the Kirchhoff indices of the random cyclooctatetraene chains and the random spiro chains.