arXiv:2007.04479v2 [math.CO] 10 Nov 2021Signless Laplacian spectral radius and matchings in graphs ∗Chang Liu, Yingui Pan, Jianping Li †College of Liberal Arts and Sciences, National University of Defense Technology,Changsha, China, 410073.November 11, 2021AbstractThe signless Laplacian ...
In this paper, we prove that ifλ1(G) nk2. As a result, we proveα′(G)≥nd2λ1(G)2+d2; we characterize when equality holds in the bound.doi:10.1016/j.ejc.2016.02.004Suil OElsevier LtdEuropean Journal of CombinatoricsS. O, Spectral radius and fractional matchings in graphs, ...
As corollaries, sufficient spectral condition for fractional perfect matchings and analogous results involving Q Q -index and A_{\\alpha} A_{\\alpha} -spectral radius are obtained, and former spectral results in [European J. Combin. 55 (2016) 144-148] are extended....
Graph eigenvalues play a fundamental role in controlling structural properties which are critical considerations in the design of supercomputing interconnection networks, such as bisection bandwidth, diameter, and fault tolerance. This motivates considering graphs with optimal spectral expansion, calledRamanujan ...
Letβ>0. Motivated by the notion of jumbled graphs introduced by Thomason, the expander mixing lemma and Haemers’s vertex separation inequality, we say that a graphGwithnvertices is a weakly(n,β)-graph if|X||Y|(n−|X|)(n−|Y|)≤β2holds for every pair of disjoint proper subs...
In this study we consider connected graphs of fixed order n and size n that minimize the largest eigenvalue of the adjacency matrix, also known as the spectral radius. Such graphs are called minimizers. The motivation for this research lies in the fact that the spectral radius plays a signif...
Spectral radiusmatchingsconnected graphs05C5005C70The matching number of G , written , is the size of a maximum matching in G . Suppose that n and k are positive integers of the same parity. Let be the largest root of and In this article, we prove that for a positive integer , if G...
In this paper, some properties between the signless Laplacian spectral radius and perfect matching in graphs are establish. Let $r(n)$ be the largest root of equation $x^3-(3n-7)x^2+n(2n-7)x-2(n^2-7n+12)=0$. We show that $G$ has a perfect matching for $n=4$ or $n\\...
O [Spectral\nradius and matchings in graphs, Linear Algebra Appl. 614 (2021) 316--324],\nwhich gives a sufficient condition for the existence of a perfect matching in a\ngraph in terms of the adjacency spectral radius.Yanhua ZhaoXueyi Huang...
For ann-vertex graphG, a fractional matching ofGis a functionfgiving each edge a real number in [0,1] such that∑e∈Γ(v)f(e)≤1\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\use...