给定直径的单圈图的边修正Szeged指标的下界  

The Lower Bound of Edge Revised Szeged Index of Unicyclic Graphs with Given Diameter

作　　者：王敏 刘蒙蒙 WANG Min;LIU Mengmeng(Institute of Applied Mathematics,Lanzhou Jiaotong University,Lanzhou,Gansu,730o70,P.R.China)

机构地区：[1]兰州交通大学应用数学研究所,甘肃兰州730070

出　　处：《数学进展》2023年第1期25-45,共21页Advances in Mathematics（China）

基　　金：国家自然科学基金(No.11961040);甘肃高等学校创新能力提升项目(No.2019A-37);兰州交通大学天佑青年托举人才计划。

摘　　要：连通图G的边修正Szeged指标Sz^(*)_(e)(G)定义为Sz^(*)_(e)(G)=∑_(e=uv∈E_(G))(mu(e|G)+m_(0)(e|G)/2)(m_(v)(e|G)+m_(0)(e|G)/2)),其中m_(u)(e|G),m_(v)(e|G),m_(0)(e|G)分别是G中到u点比到v点距离近的边的数目、到v点比到u点距离近的边的数目、以及到u,v两点距离同样近的边的数目.本文通过变换和计算得到了给定直径的单圈图的边修正Szeged指标的下界,并刻画了达到下界的极值图.Given a connected graph G,the edge revised Szeged index is defined as Sz^(*)_(e)(G)=∑_(e=uv∈E_(G))(mu(e|G)+m_(0)(e|G)/2)(m_(v)(e|G)+m_(0)(e|G)/2)),where m_(u)(e),m_(v)(e)and m_(0)(e)are the number of edges of G lying closer to vertex u than to vertex v,the number of edges of G lying closer to vertex v than to vertex u and the number of edges of G at the same distance to u and v,respectively.In this paper,by transformation and calculation,the lower bound of edge revised Szeged index of unicyclic graphs with given diameter is obtained,and the extremal graph is depicted.

关 键 词：WIENER指标 边修正Szeged指标 单圈图 极值图 

分 类 号：O157.5[理学—数学]