The expected values of Hosoya index and Merrifield-Simmons index in a random spiro chain - Huang, Guihua; Wu, Renfang; Deng, Hanyuan (Utilitas Mathematica, 2019)
The Hosoya index m(G) and the Merrifield-Simmons index t(G) of a graph G are the number of matchings and the number of independent sets in G, respectively. In this paper, we establish exact formulas for the expected values of the Hosoya index and Merrifield-Simmons index of a random spiro chain, and generalize the results of DoSlic and Litz [7]. Moreover, we obtain the average values of the Hosoya index and the Merrifield-Simmons index with respect to the set of all spiro chains with n hexagons, AMS classification: 05C12, 05C80, 05C90, 05D40. © 2019 Utilitas Mathematica Publishing Inc.. All rights reserved.