Spectral radius and fractional matchings in 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.

Spectral radius of bipartite graphs

On the distance spectral radius of unicyclic graphs with perfect matchings

Ela on the Distance Spectral Radius of Unicyclic Graphs with Perfect Matchings

Abstract. For a connected graph, the distance spectral radius is the largest eigenvalue of its distance matrix. Let U1 2k be the graph obtained from C3 by attaching a path of length n− 3 at one vertex. Let U2 2k be the graph obtained from C3 by attaching a pendant edge together with k − 2 paths of length 2 at the same vertex. In this paper, it is proved that U1 2k (resp., U 2 2k) is the unique ...

On the Signless Laplacian Spectral Radius of Bicyclic Graphs with Perfect Matchings

The graph with the largest signless Laplacian spectral radius among all bicyclic graphs with perfect matchings is determined.