Maximal graphs with a prescribed complete bipartite graph as a star complement

被引：3

作者：

Fang, Xiaona ^{[1
]}

You, Lihua ^{[1
]}

Huang, Yufei ^{[2
]}

机构：

[1] South China Normal Univ, Sch Math Sci, Guangzhou 510631, Peoples R China

[2] Guangzhou Civil Aviat Coll, Dept Math Teaching, Guangzhou 510403, Peoples R China

来源：

AIMS MATHEMATICS | 2021年 / 6卷 / 07期

基金：

中国国家自然科学基金;

关键词：

adjacency eigenvalue; star set; star complement; maximal graph; REGULAR GRAPHS; LINE GRAPHS;

D O I：

10.3934/math.2021419

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

Let G be a graph of order n and mu be an adjacency eigenvalue of G with multiplicity k >= 1. A star complement for mu in G is an induced subgraph of G of order n - k with no eigenvalue mu. In this paper, we characterize the maximal graphs with the bipartite graph K-2,K-s as a star complement for eigenvalues mu = -2,1 and study the cases of other eigenvalues for further research.

引用

页码：7153 / 7169

页数：17

共 18 条

[1] Asgharsharghi L, 2015, ARS COMBINATORIA, V122, P431
[2] Characterizing line graphs by star complements
Bell, FK
[J]. LINEAR ALGEBRA AND ITS APPLICATIONS, 1999, 296 (1-3) : 15 - 25
[3] Line graphs of bipartite graphs with Hamiltonian paths
Bell, FK
[J]. JOURNAL OF GRAPH THEORY, 2003, 43 (02) : 137 - 149
[4] Cvetkovi D., 1980, Spectra of graphs theory and application
[5] Some characterizations of graphs by star complements
Cvetkovic, D
Rowlinson, P
Simic, SK
[J]. LINEAR ALGEBRA AND ITS APPLICATIONS, 1999, 301 (1-3) : 81 - 97
[6] Cvetkovic D., 2010, London Mathematical Society Student Texts, V75
[7] Cvetkovic Dragos, 1997, Eigenspaces of graphs
[8] On graphs with complete bipartite star complements
Jackson, PS
Rowlinson, P
[J]. LINEAR ALGEBRA AND ITS APPLICATIONS, 1999, 298 (1-3) : 9 - 20
[9] Ramezani F, 2014, ARS COMBINATORIA, V116, P129
[10] An extension of the star complement technique for regular graphs
Rowlinson, Peter
[J]. LINEAR ALGEBRA AND ITS APPLICATIONS, 2018, 557 : 496 - 507

← 1 2 →