A lower bound on the least signless Laplacian eigenvalue of a graph
نویسندگان
چکیده
منابع مشابه
A sharp lower bound for the least eigenvalue of the signless Laplacian of a non-bipartite graph
We prove that the minimum value of the least eigenvalue of the signless Laplacian of a connected nonbipartite graph with a prescribed number of vertices is attained solely in the unicyclic graph obtained from a triangle by attaching a path at one of its endvertices. © 2008 Elsevier Inc. All rights reserved. AMS classification: 05C50
متن کاملOn the least signless Laplacian eigenvalue of a non-bipartite connected graph with fixed maximum degree
In this paper, we determine the unique graph whose least signless Laplacian eigenvalue attains the minimum among all non-bipartite unicyclic graphs of order n with maximum degree Δ and among all non-bipartite connected graphs of order n with maximum degree Δ, respectively.
متن کاملEla on the Least Signless Laplacian Eigenvalue of Some Graphs
For a graph, the least signless Laplacian eigenvalue is the least eigenvalue of its signless Laplacian matrix. This paper investigates how the least signless Laplacian eigenvalue of a graph changes under some perturbations, and minimizes the least signless Laplacian eigenvalue among all the nonbipartite graphs with given matching number and edge cover number, respectively.
متن کاملOn the Average Eccentricity, the Harmonic Index and the Largest Signless Laplacian Eigenvalue of a Graph
The eccentricity of a vertex is the maximum distance from it to another vertex and the average eccentricity ecc (G) of a graph G is the mean value of eccentricities of all vertices of G. The harmonic index H (G) of a graph G is defined as the sum of 2 di+dj over all edges vivj of G, where di denotes the degree of a vertex vi in G. In this paper, we determine the unique tree with minimum average...
متن کاملThe smallest eigenvalue of the signless Laplacian
Recently the signless Laplacian matrix of graphs has been intensively investigated. While there are many results about the largest eigenvalue of the signless Laplacian, the properties of its smallest eigenvalue are less well studied. The present paper surveys the known results and presents some new ones about the smallest eigenvalue of the signless Laplacian.
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
ژورنال
عنوان ژورنال: Linear Algebra and its Applications
سال: 2014
ISSN: 0024-3795
DOI: 10.1016/j.laa.2014.01.015