Ordering Quasi-Tree Graphs on n Vertices by Their Spectral Radii

摘要

A connected graph G =(V,E) is called a quasi-tree graph,if there exists a vertex vo ∈ V(G) such that G-v0 is a tree.Liu and Lu [Linear Algebra Appl.428 (2008) 2708-2714] determined the maximal spectral radius together with the corresponding graph among all quasi-tree graphs on n vertices.In this paper,we extend their result,and determine the second to the fifth largest spectral radii together with the corresponding graphs among all quasi-tree graphs on n vertices.