两类联图的PI不变边  

PI invariant edges of two union graphs

作　　者：熊金 李怡博 XIONG Jin;LI Yibo(Faculty of Mathematics and Statistics,Hubei University,Wuhan 430062,China)

机构地区：[1]湖北大学数学与统计学学院,湖北武汉430062

出　　处：《湖北大学学报（自然科学版）》2024年第1期45-51,共7页Journal of Hubei University：Natural Science

基　　金：国家自然科学基金面上项目(11971158)资助。

摘　　要：设G=(V(G),E(G))是一个简单连通图。图G的PI指标定义为PI(G)=∑_(e=uv∈E(G))[n_(1)^((e|G))+n_(2)^((e|G))],其中n_(1)^((e|G))是图G中到点u的距离比到点v的距离小的点的数目,n_(2)^((e|G))是图G中到点v的距离比到点u的距离小的点的数目。如果PI(G-e)=PI(G),那么边e称为图G的PI不变边。本文中分别讨论门槛图和轮图存在PI不变边的条件。Let G=(V(G),E(G))be a simple connected graph.The PI-index of G is defined as PI(G)=∑_(e=uv∈E(G))[n_(1)^((e|G))+n_(2)^((e|G))],where n_(1)^((e|G))is the number of vertices in G lying closer to the vertex u than to the vertex v and n_(2)^((e|G))is the number of vertices in G lying closer to the vertex v than to the vertex u.If PI(G-e)=PI(G)for some e∈E(G),then we call the edge e PI invariant of G.In this paper,we studied the existence of PI invariant edges in threshold graphs and wheel graphs,respectively.

关 键 词：PI指标 联图 门槛图 轮图 PI不变边 

分 类 号：O157[理学—数学]