给定悬挂点数的树和单圈图的顶点度函数研究  

Research on vertex-degree function index for trees and unicyclic graphswith given number of pendant vertex

作　　者：陈诗琴 耿显亚 CHEN Shiqin;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）》2024年第3期350-353,共4页Journal of Harbin University of Commerce：Natural Sciences Edition

基　　金：国家自然科学基金项目(12171190);安徽省自然科学基金(2008085MA01)。

摘　　要：设G是n阶简单图,G的悬挂点数记作p(G),顶点度函数指数H_(f)(G)定义为H_(f)(G)=∑_(v∈V(G))f(d(v)).考虑在给定悬挂点数为k的n阶树和单圈图中,在f(x)是严格凸函数的情况下,顶点度函数H_(f)(G)的最大值问题.在f(x)是严格凹函数的情况下,同样的结果也适用于顶点度函数H_(f)(G)的最小值问题.通过对这些情况的分析,得出了顶点度函数H_(f)(G)在给定条件下的最值性质.这些结果对理解图论中的悬挂点和顶点度函数的性质具有重要意义.Let G be a simple graph of order n,the number of pendant vertices of G is denoted by p(G),and the vertex-degree function index H_(f)(G)was defined as H_(f)(G)=∑_(v∈V(G))f(d(v)).This paper explored the maximum value problem of the vertex degree function index H_(f)(G)for trees T and unicyclic graphs G of order n and the number of pendant vertices k for strictly convex functions f(x).The same results were valid for the corresponding minimization problem when f(x)was strictly concave and the inequality was reversed.Through careful analysis of these scenarios,established the extremal properties of the vertex degree function within the specified conditions.These findings hold significant importance in elucidating the properties of pendant vertices and vertex degree functions in graph theory.

关 键 词：树 单圈图 悬挂点 严格凸函数 严格凹函数 顶点度函数 

分 类 号：O157.6[理学—数学]