Integral trees of diameter 4

Mohr, SH; Macdougall, J

Integral trees of diameter 4

Mohr, SH Macdougall, J

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Publisher:: Kalasalingam University
Publication Type:: Journal Article
Citation:: AKCE : International journal of graphs and combinatorics, 2010, 7 (2), pp. 171 - 188
Issue Date:: 2010-01

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Field	Value	Language
dc.contributor.author	Mohr, SH	en_US
dc.contributor.author	Macdougall, J	en_US
dc.date.issued	2010-01	en_US
dc.identifier.citation	AKCE : International journal of graphs and combinatorics, 2010, 7 (2), pp. 171 - 188	en_US
dc.identifier.issn	0972-8600	en_US
dc.identifier.uri	http://hdl.handle.net/10453/14488
dc.description.abstract	An integral tree is a tree whose adjacency matrix has only integer eigenvalues. While most previous work by other authors has been focused either on the very restricted case of balanced trees or on finding trees with diameter as large as possible, we study integral trees of diameter 4. In particular, we characterize all diameter 4 integral trees of the form T(m1, t1) T(m2, t2). In addition we give elegant parametric descriptions of infinite families of integral trees of the form T(m1, t1) · · · T(mn, tn) for any n > 1. We conjecture that we have found all such trees.	en_US
dc.publisher	Kalasalingam University	en_US
dc.relation.ispartof	AKCE : International journal of graphs and combinatorics	en_US
dc.relation.isbasedon	10.2298/FIL1402241P	en_US
dc.title	Integral trees of diameter 4	en_US
dc.type	Journal Article
utslib.citation.volume	2	en_US
utslib.citation.volume	7	en_US
utslib.for	0101 Pure Mathematics	en_US
pubs.embargo.period	Not known	en_US
pubs.organisational-group	/University of Technology Sydney
pubs.organisational-group	/University of Technology Sydney/DVC (Research)
pubs.organisational-group	/University of Technology Sydney/DVC (Research)/Institute For Sustainable Futures
utslib.copyright.status	open_access
pubs.consider-herdc	false	en_US
pubs.issue	2	en_US
pubs.volume	7	en_US

Abstract:

An integral tree is a tree whose adjacency matrix has only integer eigenvalues. While most previous work by other authors has been focused either on the very restricted case of balanced trees or on finding trees with diameter as large as possible, we study integral trees of diameter 4. In particular, we characterize all diameter 4 integral trees of the form T(m1, t1) T(m2, t2). In addition we give elegant parametric descriptions of infinite families of integral trees of the form T(m1, t1) · · · T(mn, tn) for any n > 1. We conjecture that we have found all such trees.

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http://hdl.handle.net/10453/14488