中北大学学报（自然科学版）2024，Vol.45Issue(1)：30-35,6.DOI:10.3969/j.issn.1673-3193.2024.01.004
给定悬挂点个数的分子树的ISDD指数的极值
Extremal ISDD Index of Molecular Trees with Fixed Number of Pendent Vertices
摘要
Abstract
Let G=(V(G),E(G))be a connected graph of order n,V(G)be vertex set of G,E(G)be edge set of G,deg(x)be degree of the vertex x.The inverse symmetric division deg index of G is ISDD(G)=∑xy∈E(G)(deg(x)·deg(y)/deg(x)2+deg(y)2).Inequality and classification discussion are used to study the ISDD(G)of molecular tree with fixed number of pendent vertices,respectively,the extreme value of the ISDD index of the molecular tree with the number of pendent vertices is even number and the number of pendent vertices is more than or equal to 3 are discussed,the tree whose vertex degree is less than 4 is called molecular tree.Firstly,the minimum value of the inverse symmetric division deg index of G is determined when the number of pendent vertices is even,that is ISDD(MT)=1/2 n-31/85 p-1/10.Sec-ondly,when the number of pendent vertices is greater than or equal to 3,the maximum value of the inverse symmetric division deg index of G in the molecular tree is determined,that is ISDD(MT)=1/2 n-9/65 p-1/2,and the molecular tree of ISDD index reaching the extreme value is described.关键词
图/反对称分割指数(ISDD指数)/悬挂点/分子树Key words
graph/inverse symmetric division deg index(ISDD index)/pendent vertex/molecular tree分类
数理科学引用本文复制引用
赵芳方,邵燕灵..给定悬挂点个数的分子树的ISDD指数的极值[J].中北大学学报（自然科学版）,2024,45(1):30-35,6.基金项目
山西省自然科学基金资助项目(201901D211227) （201901D211227）
