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Please use this identifier to cite or link to this item: http://hdl.handle.net/1959.13/932147

Title: Integral trees of diameter 4
Author/Creator: Mohr, Steve; MacDougall, Jim
Institution: The University of Newcastle. Faculty of Science & Information Technology, School of Mathematical and Physical Sciences
Description: 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.
Relation: AKCE International Journal of Graphs and Combinatorics Vol. 7, Issue 2, p. 171-188
Relation: http://www.akcejournal.org/index.html
Date: 2010
Publisher: Arulmigu Kalasalingam College of Engineering
Keyword(s): integral graphs; integral trees; balanced trees
Resource Type: journal article
Identifier: http://hdl.handle.net/1959.13/932147
Identifier: ISSN:0972-8600

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