Authors: Simić, Slobodan 
Živković, Dejan
Anđelić, Milica
da Fonseca, Carlos
Title: Reflexive line graphs of trees
Journal: Journal of Algebraic Combinatorics
Volume: 43
Issue: 2
First page: 447
Last page: 464
Issue Date: 1-Mar-2016
Rank: M21
ISSN: 0925-9899
DOI: 10.1007/s10801-015-0640-z
A graph is reflexive if the second largest eigenvalue of its adjacency matrix is less than or equal to 2. In this paper, we characterize trees whose line graphs are reflexive. It turns out that these trees can be of arbitrary order—they can have either a unique vertex of arbitrary degree or pendant paths of arbitrary lengths, or both. Since the reflexive line graphs are Salem graphs, we also relate some of our results to the Salem (graph) numbers.
Keywords: Adjacency matrix | Line graph | Reflexive graph | Salem graph | Second largest eigenvalue | Subdivision graph
Publisher: Springer Link

Show full item record


checked on Jul 21, 2024

Page view(s)

checked on May 10, 2024

Google ScholarTM




Items in DSpace are protected by copyright, with all rights reserved, unless otherwise indicated.