随机仙人掌Hosoya指数和Merrifield-Simmons指数的期望值
The Expected Values of Hosoya Index and Merrifield-Simmons Index of Random Hexagonal Cacti
摘要：
Hosoya指数和Merrifield-Simmons指数是反映苯型烃类化合物的一些物理性质（例如沸点或生成热）的两个著名的拓扑描述符。本文建立了随机六角仙人掌这两个指标的期望值的母函数。这推广了Doslic和Maloy在2010年发表在离散数学上的结果。利用亚纯函数和幂级数增长性的思想，建立了随机仙人掌上这些指标的渐近性态。
英文摘要：
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.
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