摘要
设G是一个n阶连通图,H(G)是图G的Harmonic矩阵,图G的Harmonic能量定义为矩阵H(G)的所有特征值的绝对值之和。设e=xy是图G的一条边,G-e表示从图G中删除边e=xy得到的图,d_(x)表示顶点x的度。本文讨论了当删除一条非悬挂边e=xy且N_(G)(x)∩N_(G)(y)=■时,连通图G的Harmonic能量的变化。当d_(x),d_(y)≥d时,Harmonic能量变化的上界为2/d√1+16(d-1)/(d+1)^(2);当d_(x),d_(y)≥2时,Harmonic能量变化的上界为5/3。
Let G be a connected graph with n vertices and H(G)be the Harmonic matrix of graph G.The Harmonic energy of graph G is the sum of the absolute values of the eigenvalues of matrix H(G).Let e=xy be an edge of graph G,G-e denotes the graph obtained from G by removing the edge e=xy and d_(x) denotes the degree of vertex x.In this paper,we discussed the change of Harmonic energy when removing a non-pendant edge e=xy with N_(G)(x)∩N_(G)(y)=■.Meanwhile,its upper bound was given.If d_(x),d_(y)≥d,the upper bound is 2/d√1+16(d-1)/(d+1)^(2);if d_(x),d_(y)≥2,it is 5/3.
作者
胡文静
高玉斌
HU Wenjing;GAO Yubin(School of Mathematics,North University of China,Taiyuan 030051,China)
出处
《中北大学学报（自然科学版）》
CAS
2023年第2期104-108,共5页
Journal of North University of China(Natural Science Edition)
基金
山西省自然科学基金资助项目(201901D211227)。
