高校应用数学学报A辑
高校應用數學學報A輯
고교응용수학학보A집
APPLIED MATHEMATICS A JOURNAL OF CHINESE UNIVERSITIES
2014年
1期
105-114
,共10页
谱矩%字典序%树%单圈图%双圈图
譜矩%字典序%樹%單圈圖%雙圈圖
보구%자전서%수%단권도%쌍권도
spectral moment%lexicographical order%tree%unicyclic graph%bicyclic graph
设G =(V (G), E (G))是一个n阶简单图, V (G), E (G)分别为图G的顶点集和边集. G的k阶谱矩sk(G)为G的所有特征值λ1,λ2,···,λn的k次幂之和,即sk(G)=Pn i=1λik.该文首先列出图的五种变换,然后得到了其对任意图的零到四阶谱矩的变化规律,最后依次给出了树和单圈图依谱矩序列S4的字典序分别排在前4-6位和后4-6的图及其特征以及双圈图依谱矩序列S4的字典序排在前6位和后6位的图及其特征.
設G =(V (G), E (G))是一箇n階簡單圖, V (G), E (G)分彆為圖G的頂點集和邊集. G的k階譜矩sk(G)為G的所有特徵值λ1,λ2,···,λn的k次冪之和,即sk(G)=Pn i=1λik.該文首先列齣圖的五種變換,然後得到瞭其對任意圖的零到四階譜矩的變化規律,最後依次給齣瞭樹和單圈圖依譜矩序列S4的字典序分彆排在前4-6位和後4-6的圖及其特徵以及雙圈圖依譜矩序列S4的字典序排在前6位和後6位的圖及其特徵.
설G =(V (G), E (G))시일개n계간단도, V (G), E (G)분별위도G적정점집화변집. G적k계보구sk(G)위G적소유특정치λ1,λ2,···,λn적k차멱지화,즉sk(G)=Pn i=1λik.해문수선렬출도적오충변환,연후득도료기대임의도적령도사계보구적변화규률,최후의차급출료수화단권도의보구서렬S4적자전서분별배재전4-6위화후4-6적도급기특정이급쌍권도의보구서렬S4적자전서배재전6위화후6위적도급기특정.
Let G = (V (G), E(G)) be a simple graph with n vertices and m edges. The kth spectral moments of G is given by sk(G)=Pni=1λik, where λ1,λ2, · · · ,λn, are the eigenvalues of the adjacency matrix of G. In this paper, the variation properties of the spectral moments are studied by using five kinds of transformations. The lexicographical ordering of trees, unicyclic graphs and bicyclic graphs with respect to the sequence S4 are obtained respectively. The first fourth to sixth and the last fourth to the last sixth trees and unicyclic graphs with respect to the sequence S4 are characterized, and the first six and the last six bicyclic graphs with respect to the sequence S4 are characterized.
