WSEAS Transactions on Mathematics
Print ISSN: 1109-2769, E-ISSN: 2224-2880
Volume 12, 2013
On Further Ordering Bicyclic Graphs with Respect to the Laplacian Spectra Radius
Authors: ,
Abstract: Among all the n-vertex bicyclic graphs, the first eight largest Laplacian spectra radii had been obtained in the past, all of which are no smaller than n − 1. In this paper, it is first obtained that all the bicyclic graphs on n vertices with Laplacian spectra radii at least n − 2 must contain two adjacent vertices which cover all the vertices except possibly two and one of the two adjacent vertices must have the degree at least n−3. Then the total forty-two such graphs are further ordered, and the ninth to the forty-first largest Laplacian spectra radii among all the n-vertex bicyclic graphs are finally determined in this way.