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Integral trees of odd diameters
Author(s) -
Ghorbani E.,
Mohammadian A.,
TayfehRezaie B.
Publication year - 2012
Publication title -
journal of graph theory
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.164
H-Index - 54
eISSN - 1097-0118
pISSN - 0364-9024
DOI - 10.1002/jgt.20619
Subject(s) - mathematics , integral graph , adjacency matrix , combinatorics , eigenvalues and eigenvectors , graph , integer (computer science) , adjacency list , discrete mathematics , line graph , graph power , physics , computer science , quantum mechanics , programming language
A graph is called integral if all eigenvalues of its adjacency matrix consist entirely of integers. Recently, Csikvári proved the existence of integral trees of any even diameter. In the odd case, integral trees have been constructed with diameter at most 7. In this article, we show that for every odd integer n >1, there are infinitely many integral trees of diameter n . © 2011 Wiley Periodicals, Inc. J Graph Theory