Hamilton图的Wiener型指标
发布时间：2019-04-23 13:12
【摘要】：在化学理论中,拓扑指标可以用来理解混合物的物理和化学性质,不同的指标反映了分子的不同性能.分子拓扑指标以及分子图的不变量的研究是化学图论中的研究领域之一.简单无向图G=(V,E)的每个顶点代表分子中的一个原子,每条边代表原子间形成的化学键,这种图就叫做分子图.分子图中顶点数、边数等都可以作为分子中的一些稳定不变量.在实际应用中,通常用不同的数值来描述分子的不同的可测量的物理化学性质,所以为了将分子的拓扑性质与分子的可测量的物理化学性质联系起来,很有必要引入一些可以用数值表示的量,并且他们与分子图中的某些性质有关,分子拓扑指标在物理、化学和生物等许多学科有重要的用途.Wiener指标是被广泛研究的拓扑指标之一,它不仅是与有机化合物的物理化学性质关系紧密的早期拓扑指标,更是许多数学家和化学家的一个研究主题.Wiener指标[25]是连通图G中所有无序点对的距离和,即W(G)=∑{u,v}?VdG(u, v) =12∑(u,v)∈V×VdG(u,v),其中dG(u,v)表示G中u到v的距离.连通图G的hyper-Wiener指标定义为WW(G)=12W(G)+1在文献[12,13]中,Gutman等人提出了乘积版本的Wiener指标(也叫做π指标):π(G)=Π{u,v}?V(G)dG(u,v).令Hn是所有n点Hamilton图组成的集合.本文刻画了Hn中具有第i小(1≤i≤n-2)Wiener,hyper-Wiener和π指标的图.更进一步,我们也刻画了Hn中具有最大,第二大,第三大Wiener,hyper-Wiener和π指标的图,并给出了相应的指标计算公式.
[Abstract]:In chemical theory, topological indices can be used to understand the physical and chemical properties of mixtures, and different indices reflect the different properties of molecules. The study of molecular topological indices and invariants of molecular graphs is one of the research fields in chemical graph theory. Each vertex of a simple undirected graph G = (V, E) represents an atom in the molecule, and each edge represents the chemical bonds formed between the atoms. This graph is called a molecular graph. The number of vertices and edges in the molecular graph can be regarded as some stable invariants in the molecule. In practical applications, different values are usually used to describe the different measurable physical and chemical properties of molecules, so in order to relate the topological properties of molecules to the measurable physical and chemical properties of molecules, It is necessary to introduce some quantities that can be expressed numerically, and they are related to some of the properties of the molecular graph, and the molecular topological indices are in physics, Wiener index is one of the topological indexes widely studied. It is not only an early topological index closely related to the physical and chemical properties of organic compounds, but also an early topological index which is closely related to the physical and chemical properties of organic compounds. Wiener index [25] is the distance sum of all disordered point pairs in connected graph G, that is, W (G) = 鈭，
本文编号：2463498
[Abstract]:In chemical theory, topological indices can be used to understand the physical and chemical properties of mixtures, and different indices reflect the different properties of molecules. The study of molecular topological indices and invariants of molecular graphs is one of the research fields in chemical graph theory. Each vertex of a simple undirected graph G = (V, E) represents an atom in the molecule, and each edge represents the chemical bonds formed between the atoms. This graph is called a molecular graph. The number of vertices and edges in the molecular graph can be regarded as some stable invariants in the molecule. In practical applications, different values are usually used to describe the different measurable physical and chemical properties of molecules, so in order to relate the topological properties of molecules to the measurable physical and chemical properties of molecules, It is necessary to introduce some quantities that can be expressed numerically, and they are related to some of the properties of the molecular graph, and the molecular topological indices are in physics, Wiener index is one of the topological indexes widely studied. It is not only an early topological index closely related to the physical and chemical properties of organic compounds, but also an early topological index which is closely related to the physical and chemical properties of organic compounds. Wiener index [25] is the distance sum of all disordered point pairs in connected graph G, that is, W (G) = 鈭，
本文编号：2463498
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