The maximum spectral radius of t-connected graphs with bounded matching number

2022 ◽  
Vol 345 (4) ◽  
pp. 112775
Author(s):  
Wenqian Zhang
Keyword(s):  
Spectral Radius ◽  
Matching Number ◽  
Connected Graphs

scholarly journals On spectral radius of the distance matrix

2010 ◽  
Vol 4 (2) ◽  
pp. 269-277 ◽  
Author(s):  
Zhongzhu Liu
Keyword(s):  
Spectral Radius ◽  
Chromatic Number ◽  
Distance Matrix ◽  
Matching Number ◽  
Vertex Connectivity ◽  
Connected Graphs

We characterize graphs with minimal spectral radius of the distance matrix in three classes of simple connected graphs with n vertices: with fixed vertex connectivity, matching number and chromatic number, respectively.

scholarly journals Matchings, Cycle Bases, and the Maximum Genus of a Graph

10.37236/2479 ◽  
2012 ◽  
Vol 19 (3) ◽  
Author(s):  
Michal Kotrbčík ◽  
Martin Škoviera
Keyword(s):  
Spanning Tree ◽  
Spanning Trees ◽  
Perfect Matching ◽  
Intersection Graph ◽  
Matching Number ◽  
Maximum Genus ◽  
Cycle Space ◽  
Intersection Graphs ◽  
Connected Graphs ◽  
Cycle Bases

We study the interplay between the maximum genus of a graph and bases of its cycle space via the corresponding intersection graph. Our main results show that the matching number of the intersection graph is independent of the basis precisely when the graph is upper-embeddable, and completely describe the range of matching numbers when the graph is not upper-embeddable. Particular attention is paid to cycle bases consisting of fundamental cycles with respect to a given spanning tree. For $4$-edge-connected graphs, the intersection graph with respect to any spanning tree (and, in fact, with respect to any basis) has either a perfect matching or a matching missing exactly one vertex. We show that if a graph is not $4$-edge-connected, different spanning trees may lead to intersection graphs with different matching numbers. We also show that there exist $2$-edge connected graphs for which the set of values of matching numbers of their intersection graphs contains arbitrarily large gaps.

Distance spectral radius of unicyclic graphs with fixed maximum degree

2019 ◽  
Vol 19 (04) ◽  
pp. 2050068
Author(s):  
Hezan Huang ◽  
Bo Zhou
Keyword(s):  
Spectral Radius ◽  
Connected Graph ◽  
Maximum Degree ◽  
Distance Matrix ◽  
The Other ◽  
Connected Graphs ◽  
Largest Eigenvalue ◽  
Unicyclic Graphs ◽  
The Largest Eigenvalue

The distance spectral radius of a connected graph is the largest eigenvalue of its distance matrix. For integers [Formula: see text] and [Formula: see text] with [Formula: see text], we prove that among the connected graphs on [Formula: see text] vertices of given maximum degree [Formula: see text] with at least one cycle, the graph [Formula: see text] uniquely maximizes the distance spectral radius, where [Formula: see text] is the graph obtained from the disjoint star on [Formula: see text] vertices and path on [Formula: see text] vertices by adding two edges, one connecting the star center with a path end, and the other being a chord of the star.

scholarly journals The Smallest Spectral Radius of Graphs with a Given Clique Number

2014 ◽  
Vol 2014 ◽  
pp. 1-9
Author(s):  
Jing-Ming Zhang ◽  
Ting-Zhu Huang ◽  
Ji-Ming Guo
Keyword(s):  
Spectral Radius ◽  
Maximum Clique ◽  
Clique Number ◽  
Connected Graphs

The first four smallest values of the spectral radius among all connected graphs with maximum clique sizeω≥2are obtained.

scholarly journals On sufficient spectral radius conditions for hamiltonicity of k-connected graphs

2020 ◽  
Vol 604 ◽  
pp. 129-145
Author(s):  
Qiannan Zhou ◽  
Hajo Broersma ◽  
Ligong Wang ◽  
Yong Lu
Keyword(s):  
Spectral Radius ◽  
Connected Graphs

The distance spectral radius of graphs with given number of odd vertices

2016 ◽  
Vol 31 ◽  
pp. 286-305 ◽  
Author(s):  
Hongying Lin ◽  
Bo Zhou
Keyword(s):  
Spectral Radius ◽  
Connected Graphs

The graphs with smallest, respectively largest, distance spectral radius among the connected graphs, respectively trees with a given number of odd vertices, are determined. Also, the graphs with the largest distance spectral radius among the trees with a given number of vertices of degree 3, respectively given number of vertices of degree at least 3, are determined. Finally, the graphs with the second and third largest distance spectral radius among the trees with all odd vertices are determined.

On the distance signless Laplacian spectral radius of graphs and digraphs

2017 ◽  
Vol 32 ◽  
pp. 438-446 ◽  
Author(s):  
Dan Li ◽  
Guoping Wang ◽  
Jixiang Meng
Keyword(s):  
Spectral Radius ◽  
Connected Graph ◽  
Minimum Degree ◽  
Extremal Graph ◽  
Minimal Distance ◽  
Vertex Connectivity ◽  
Laplacian Spectral Radius ◽  
Connected Graphs ◽  
Signless Laplacian Spectral Radius ◽  
Signless Laplacian

Let \eta(G) denote the distance signless Laplacian spectral radius of a connected graph G. In this paper,bounds for the distance signless Laplacian spectral radius of connected graphs are given, and the extremal graph with the minimal distance signless Laplacian spectral radius among the graphs with given vertex connectivity and minimum degree is determined. Furthermore, the digraph that minimizes the distance signless Laplacian spectral radius with given vertex connectivity is characterized.

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