On the Maximal-Adjacency-Spectrum Unicyclic Graphs with Given Maximum Degree

Abstract EN

In this paper, we study the properties and structure of the maximal-adjacency-spectrum unicyclic graphs with given maximum degree.

We obtain some necessary conditions on the maximal-adjacency-spectrum unicyclic graphs in the set of unicyclic graphs with n vertices and maximum degree Δ and describe the structure of the maximal-adjacency-spectrum unicyclic graphs in the set.

Besides, we also give a new upper bound on the adjacency spectral radius of unicyclic graphs, and this new upper bound is the best upper bound expressed by vertices n and maximum degree Δ from now on.