%0 Journal Article
%T Some Bicyclic Graphs Having 2 as Their Laplacian Eigenvalues
%J Mathematics | An Open Access Journal from MDPI
%D 2019
%R https://doi.org/10.3390/math7121233
%X If G is a graph, its Laplacian is the difference between the diagonal matrix of its vertex degrees and its adjacency matrix. A one-edge connection of two graphs G 1 and G 2 is a graph G = G 1 ¡Ñ u v G 2 with V ( G ) = V ( G 1 ) ¡È V ( G 2 ) and E ( G ) = E ( G 1 ) ¡È E ( G 2 ) ¡È { e = u v } where u ¡Ê V ( G 1 ) and v ¡Ê V ( G 2 ) . In this paper, we study some structural conditions ensuring the presence of 2 in the Laplacian spectrum of bicyclic graphs of type G 1 ¡Ñ u v G 2 . We also provide a condition under which a bicyclic graph with a perfect matching has a Laplacian eigenvalue 2. Moreover, we characterize the broken sun graphs and the one-edge connection of two broken sun graphs by their Laplacian eigenvalue 2. View Full-Tex
%U https://www.mdpi.com/2227-7390/7/12/1233