Spectral radius conditions for fractional [a,b]-covered graphs

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.

Some Results on Fractional Covered Graphs∗

Let G = (V (G),E(G)) be a graph. and let g, f be two integer-valued functions defined on V (G) such that g(x)≤ f (x) for all x ∈V (G). G is called fractional (g, f )-covered if each edge e of G belongs to a fractional (g, f )-factor Gh such that h(e) = 1, where h is the indicator function of Gh. In this paper, sufficient conditions related to toughness and isolated toughness for a graph to be f...

Spectral radius of bipartite graphs

Notes on Fractional k-Covered Graphs

A graph G is fractional k-covered if for each edge e of G, there exists a fractional k-factor h, such that h(e) = 1. If k = 2, then a fractional k-covered graph is called a fractional 2-covered graph. The binding number bind(G) is defined as follows, bind(G) = min{ |NG(X)| |X| : Ø = X ⊆ V (G), NG(X) = V (G)}. In this paper, it is proved that G is fractional 2-covered if δ(G) ≥ 4 and bind(G) > 5...

On 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...