The spectral radius of graphs with no odd wheels

被引：51

作者：

Cioaba, Sebastian ^{[1
]}

Desai, Dheer Noal ^{[1
]}

Tait, Michael ^{[2
]}

机构：

[1] Univ Delaware, Dept Math Sci, Newark, DE 19716 USA

[2] Villanova Univ, Dept Math & Stat, Villanova, PA 19085 USA

来源：

EUROPEAN JOURNAL OF COMBINATORICS | 2022年 / 99卷

基金：

美国国家科学基金会;

关键词：

EXTREMAL GRAPHS; PROOF; NUMBERS; BOUNDS;

D O I：

10.1016/j.ejc.2021.103420

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

The odd wheel W2k+1 is the graph formed by joining a vertex to a cycle of length 2k. In this paper, we investigate the largest value of the spectral radius of the adjacency matrix of an n-vertex graph that does not contain W2k+1. We determine the structure of the spectral extremal graphs for all k >= 2, k is not an element of{4, 5}. When k = 2, we show that these spectral extremal graphs are among the Turan-extremal graphs on n vertices that do not contain W2k+1 and have the maximum number of edges, but when k >= 9, we show that the family of spectral extremal graphs and the family of Turan-extremal graphs are disjoint. (C) 2021 Elsevier Ltd. All rights reserved.

引用

页数：19

共 36 条

[1]

Babai L, 2009, ELECTRON J COMB, V16

[2] On the spectral radius of graphs with cut vertices [J].

Berman, A ;

Zhang, XD .

JOURNAL OF COMBINATORIAL THEORY SERIES B, 2001, 83 (02) :233-240

[3] Eigenvalues of subgraphs of the cube [J].

Bollobas, Bela ;

Lee, Jonathan ;

Letzter, Shoham .

EUROPEAN JOURNAL OF COMBINATORICS, 2018, 70 :125-148

[4] ON THE SPECTRAL-RADIUS OF COMPLEMENTARY ACYCLIC MATRICES OF ZEROS AND ONES [J].

BRUALDI, RA ;

SOLHEID, ES .

SIAM JOURNAL ON ALGEBRAIC AND DISCRETE METHODS, 1986, 7 (02) :265-272

[5] A Bound on the Number of Edges in Graphs Without an Even Cycle (vol 26, pg 1, 2017) [J].

Bukh, Boris ;

Jiang, Zilin .

COMBINATORICS PROBABILITY & COMPUTING, 2017, 26 (06) :952-953

[6] The Maximum Spectral Radius of Graphs Without Friendship Subgraphs [J].

Cioaba, Sebastian ;

Feng, Lihua ;

Tait, Michael ;

Zhang, Xiao-Dong .

ELECTRONIC JOURNAL OF COMBINATORICS, 2020, 27 (04) :1-19

[7] Turan numbers for odd wheels [J].

Dzido, Tomasz ;

Jastrzebski, Andrzej .

DISCRETE MATHEMATICS, 2018, 341 (04) :1150-1154

[8] The spectral radius of graphs on surfaces [J].

Ellingham, MN ;

Zha, XY .

JOURNAL OF COMBINATORIAL THEORY SERIES B, 2000, 78 (01) :45-56

[9] EXTREMAL GRAPHS FOR INTERSECTING TRIANGLES [J].

ERDOS, P ;

FUREDI, Z ;

GOULD, RJ ;

GUNDERSON, DS .

JOURNAL OF COMBINATORIAL THEORY SERIES B, 1995, 64 (01) :89-100

[10] Spectral radius and Hamiltonicity of graphs [J].

Fiedler, Miroslav ;

Nikiforov, Vladimir .

LINEAR ALGEBRA AND ITS APPLICATIONS, 2010, 432 (09) :2170-2173

← 1 2 3 4 →