随机七边形链中两类拓扑指数的期望值研究  

Expected value of two kinds of topological indexes in random heptagonal chains

作　　者：孙玉霜 耿显亚 SUN Yushuang;GENG Xianya(School of Mathematics and Big Data,Anhui University of Science and Technology,Huainan 232001,China)

机构地区：[1]安徽理工大学数学与大数据学院,安徽淮南232001

出　　处：《哈尔滨商业大学学报（自然科学版）》2023年第4期456-461,共6页Journal of Harbin University of Commerce：Natural Sciences Edition

基　　金：安徽省自然科学基金(2008085MA01);安徽省高校自然科学基金(KJ2021A0451)。

摘　　要：设G是n阶简单图,即所考虑的都是有限简单图,设G=(V(G),E(G))是一个图,V(G)表示图的顶点集,E(G)表示图的边集,G的匹配数和独立集分别记作G的Hosoya指数和Merrifield-Simmons指数,记作m(G),i(G).根据不同连接方式画出的各类别的图形,结合给定的相关公式推出所有有着n个七边形的七边形链的Hosoya指数和Merrifield-Simmons指数的期望值公式.不同的连接方式有着不同的概率,结合推导出的两个不同指标的期望值公式,代入不同的概率,得到精确的不同连接方式下的两个指数的相关内容.进而探究出在随机七边形链中的Hosoya指数和Merrifield-Simmons指数的期望值.Let G be a simple graph of order n,then,all the graphs considered were finite simple graphs.Let G=(V(G),E(G))be a graph,V(G)represented the vertex set of the graph,and E(G)represented the edge set of the graph.The number of matchings and the number of independent sets in a graph G were called the Hosoya index m(G)and the Merrifield-Simmons index i(G).According to various graphs drawn by different linking methods,the expected values of the two indexes of all heptagonal chains with n heptagons were derived by combining the given relevant formulas.Different connection methods had different probabilities.Combined with the expected value formula of two different indexes derived,different probabilities were substituted to obtain accurate contents of two indexes under different connection methods.Furthermore,the expected values of the Hosoya index and the Merrifield-Simmons index in the random heptagonal chain were explored.

关 键 词：七边形 HOSOYA指数 MERRIFIELD-SIMMONS指数 概率 期望 平均值 

分 类 号：O157.6[理学—数学]