Abstract It is shown that the second largest eigenvalue of the adjacency matrix of any d-regular graph G containing two edges the distance between which is at least 2k + 2 is at least 2d − 1 −(2d − 1 − 1)/(k+1).
Graph Adjacency matrix Signless Laplacian Second largest eigenvalue 1. Introduction Let G=(V(G),E(G)) be a simple graph of order n=|V(G)| and size m=|E(G)|. If an edge e∈E(G) joins vertices u,v∈V(G) then, for short, uv stands for e. The adjacency matrix of G is de...
the second largest distance eigenvalueD-spectrum determinedLet G be a simple connected graph of order n and DXueZhengzhouJieZhengzhouGuoZhengzhouLitaoZhengzhouLiuZhengzhouRuifangZhengzhouLinear & Multilinear Algebra: An International Journal Publishing Articles, Reviews and Problems...
However, checking whether a particular graph is a good expander is co-NP-complete. We show that the second eigenvalue of d-regular graphs, λ2, is concentrated in an interval of width O(√d) around its mean, and that its mean is O(d3/4). The result holds under various models for...
A Graph Based Method for Generating the Fiedler Vector of Irregular Problems () Citation Context ...sed on models that partition a graph by finding an eigenvector associated with the second smallest eigenvalue of its graph Laplacian matrix using an iterative method.This eigenvector model is used...
In a certain family of graphs, a graph is called minimizing (or second minimizing) if the least eigenvalue of its adjacency matrix attains the minimum (or second minimum). In this paper, we characterize the second minimizing graph among all graphs which belong to the set of complements of ...
图特征根偶图围长Let $G$ be a simple graph with $n$ vertices, and let$\\lambda_1(G)\\geq\\lambda_2(G)\\geq\\cdots\\geq\\lambda_n(G)$ be the eigenvalues of theadjacency matrix of $G$. We call $\\lambda_2(G)$ the second largest eigenvalue of $G$.In this paper, all ...
51, NO. 1, JANUARY 2006 On Maximizing the Second Smallest Eigenvalue of a State-Dependent Graph Laplacian Yoonsoo Kim and Mehran Mesbahi Abstract—We consider the set consisting of graphs of ?xed order and will correspond to point weighted edges. The vertex set of graphs in masses and the...
The geometric multiplicity of each eigenvalue of a self-adjoint Sturm–Liouville problem is equal to its algebraic multiplicity. This is true for regular p... Q Kong,H Wu,A Zettl - 《Journal of Computational & Applied Mathematics》 被引量: 40发表: 2008年 Some inverse spectral problems for ...
two further conjectures on the independence number of fullerene graphs, as well as a new upper bound on the smallest eigenvalue of a fullerene graph.doi... LUERBIO FARIA,SULAMITA KLEIN,MATEJ STEHLIK - 《Siam Journal on Discrete Mathematics》 被引量: 18发表: 2012年 GRAPHS WITH SMALL INDEPENDEN...