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ON MULTIPLICITY OF THE LAPLACIAN EIGENVALUE 2 IN BICYCLIC GRAPHS
Author(s) : M. Farkhondeh, M. Habibi and D. A. Mojdeh
Pages : [13] - [29]
Received : November 5, 2020; Revised January 17, 2021
Communicated by : Professor Bao-Yuan Zhu
Pages : [13] - [29]
Received : November 5, 2020; Revised January 17, 2021
Communicated by : Professor Bao-Yuan Zhu
Abstract
The Laplacian matrix of a graph G is denoted by 
where 
and 
is the adjacency matrix of G. A one-edge connection of two graphs 
and 
is a graph 
with 
and 
where 
and 
In this article, we study the existence and multiplicity of Laplacian eigenvalue 2 in the bicyclic graph 
based on existence and multiplicity of this special Laplacian eigenvalue in .gif){kind=small}
and 
Examples to illustrate and delimit the results are provided.
Keywords
Laplacian eigenvalue, characteristic polynomial, multiplicity, unicyclic graph, bicyclic graph.