On graphs with maximum Harary spectral radius
نویسندگان
چکیده
منابع مشابه
On graphs whose spectral radius
The structure of graphs whose largest eigenvalue is bounded by 3 2 √ 2 (≈ 2.1312) is investigated. In particular, such a graph can have at most one circuit, and has a natural quipu structure.
متن کاملThe Spectral Radius and the Maximum Degree of Irregular Graphs
Let G be an irregular graph on n vertices with maximum degree ∆ and diameter D. We show that ∆ − λ1 > 1 nD , where λ1 is the largest eigenvalue of the adjacency matrix of G. We also study the effect of adding or removing few edges on the spectral radius of a regular graph. 1 Preliminaries Our graph notation is standard (see West [22]). For a graph G, we denote by λi(G) the i-th largest eigenval...
متن کاملSpectral radius and maximum degree of connected graphs
Given a connected irregular graph G of order n, write μ for the largest eigenvalue of its adjacency matrix, ∆ for its maximum degree, andD for its diameter. We prove that ∆− μ > 1 (D + 2)n and this bound is tight up to a constant factor. This improves previous results of Stevanović and Zhang, and extends a result of Alon and Sudakov.
متن کاملOn the spectral radius of graphs
Let G be a simple undirected graph. For v ∈ V (G), the 2-degree of v is the sum of the degrees of the vertices adjacent to v. Denote by ρ(G) and μ(G) the spectral radius of the adjacency matrix and the Laplacian matrix of G, respectively. In this paper, we present two lower bounds of ρ(G) and μ(G) in terms of the degrees and the 2-degrees of vertices. © 2004 Elsevier Inc. All rights reserved. A...
متن کاملOn the spectral radius of graphs
We characterize the graphs which achieve the maximum value of the spectral radius of the adjacency matrix in the sets of all graphs with a given domination number and graphs with no isolated vertices and a given domination number. AMS Classification: 05C35, 05C50, 05C69
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: Applied Mathematics and Computation
سال: 2015
ISSN: 0096-3003
DOI: 10.1016/j.amc.2015.05.146