In this paper, we investigate several random structures, namely two classes of random lobster trees (RLTs) and a class of random spider trees (RSTs). The first class of RLTs grow with a fixed probability, whereas those from the second class evolve in a dynamic manner underlying a flavor of semi-opposite reinforcement. For these two classes, we characterize the structure of the random graphs therein via some probabilistic methods. In addition, we look into a class of RSTs that evolve in a preferential attachment manner. We characterize the structure of RSTs by determining the exact and asymptotic distributions of the number of leaves, and by computing two kinds of topological indices.

在本文中，我们研究了几种随机结构，即两类随机龙虾树（RLTs）和一类随机蜘蛛树（RSTs）。第一类RLT以固定的概率增长，而第二类RLT以动态方式演化，从而形成了半对立增强的味道。对于这两个类别，我们通过一些概率方法来表征其中的随机图的结构。此外，我们研究了以优先依恋方式进化的一类RST。我们通过确定叶数的精确和渐近分布，并通过计算两种拓扑指数来表征RST的结构。