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

Hosoya index and Merrifield-Simmons index are two well-known topological descriptors that reflex some physical properties, such as boiling points and heat of formation, of benzenoid 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 Mathematics 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.