论文标题
树木的关系和基于子图的拓扑指数
A relation on trees and the topological indices based on subgraph
论文作者
论文摘要
拓扑指数反映了分子的物理，化学和结构特性，其研究在分子拓扑，化学图理论和数学化学中具有重要作用。表征具有相同拓扑指数值的非同态图是一个自然的问题。 By introducing a relation on trees with respect to edge division vectors, denoted by $\langle\mathcal{T}_n, \preceq \rangle$, in this paper we give some results for the relation order in $\langle\mathcal{T}_n, \preceq \rangle$, it allows us to compare the size of the topological index value without relying on它们的特定形式，自然而然地，我们可以确定哪些树具有相同的拓扑指数值。基于这些结果，我们表征了一些由它们的边缘分裂矢量唯一决定的树，并构建具有相同拓扑指数值的无限型非同构树，尤其是完全确定$ 10 $的订单树。
A topological index reflects the physical, chemical and structural properties of a molecule, and its study has an important role in molecular topology, chemical graph theory and mathematical chemistry. It is a natural problem to characterize non-isomorphic graphs with the same topological index value. By introducing a relation on trees with respect to edge division vectors, denoted by $\langle\mathcal{T}_n, \preceq \rangle$, in this paper we give some results for the relation order in $\langle\mathcal{T}_n, \preceq \rangle$, it allows us to compare the size of the topological index value without relying on the specific forms of them, and naturally we can determine which trees have the same topological index value. Based on these results we characterize some classes of trees that are uniquely determined by their edge division vectors and construct infinite classes of non-isomorphic trees with the same topological index value, particularly such trees of order no more than $10$ are completely determined.
