The Expected Values of Hosoya Index and Merrifield-Simmons Index of Random Hexagonal Cacti

Hosoya index and Merrifield-Simmons index are two well-known topological descriptors that reflex some physical properties, boiling point or heat of formation for instance, of bezenoid hydrocarbon compounds. In this paper, we establish the generating functions of the expected values of these two indices of random hexagonal cacti. This generalizes the results of Doslic and Maloy, published in Discrete Mathemaics, in 2010. By applying the ideas on meromorphic functions and the growth of power series coefficients, the asymptotic behaviors of these indices on the random cacti have been established.