Spectral characterizations of graphs with small spectral radius

Graphs with Small Independence Number Minimizing the spectral radius

The independence number of a graph is defined as the maximum size of a set of pairwise non-adjacent vertices and the spectral radius is defined as the maximum eigenvalue of the adjacency matrix of the graph. Xu et al. in [The minimum spectral radius of graphs with a given independence number, Linear Algebra and its Applications 431 (2009) 937–945] determined the connected graphs of order n with...

Spectral characterizations of sandglass graphs

The sandglass graph is obtained by appending a triangle to each pendant vertex of a path. It is proved that sandglass graphs are determined by their adjacency spectra as well as their Laplacian spectra. © 2009 Elsevier Ltd. All rights reserved.

Spectral Characterizations of Dumbbell Graphs

A dumbbell graph, denoted by Da,b,c, is a bicyclic graph consisting of two vertexdisjoint cycles Ca, Cb and a path Pc+3 (c > −1) joining them having only its end-vertices in common with the two cycles. In this paper, we study the spectral characterization w.r.t. the adjacency spectrum of Da,b,0 (without cycles C4) with gcd(a, b) > 3, and we complete the research started in [J.F. Wang et al., A ...

Spectral radius of bipartite 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.