Reflexive line graphs of trees

Časopis: JOURNAL OF ALGEBRAIC COMBINATORICS

Volume, no: 43 , 2

ISSN: 0925-9899

Stranice: 447-464

Link: https://link.springer.com/article/10.1007/s10801-015-0640-z

Apstrakt:
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.
Ključne reči: Line graph, Subdivision graph, Adjacency matrix, Second largest eigenvalue, Reflexive graph, Salem graph
Kategorije objave: Bibliografske reference nastavnika Univerziteta Singidunum