Extremal unicyclic graphs with minimal distance spectral radius

Extremal unicyclic graphs with minimal distance spectral radius

The distance spectral radius ρ(G) of a graph G is the largest eigenvalue of the distance matrix D(G). Let U (n,m) be the class of unicyclic graphs of order n with given matching number m (m 6= 3). In this paper, we determine the extremal unicyclic graph which has minimal distance spectral radius in U (n,m) \ Cn.

Order unicyclic mixed graphs by spectral radius

On the spectral radius of unicyclic graphs with fixed girth

The spectral radius of a graph is the largest eigenvalue of its adjacency matrix. Let U g n be the set of unicyclic graphs of order n with girth g. For all integers n and g with 5 ≤ g ≤ n − 6, we determine the first ⌊ g2⌋+ 3 spectral radii of unicyclic graphs in the set U g n .

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 distance spectral radius of unicyclic graphs with perfect matchings