Constructions for type I trees with nonisomorphic Perron branches |
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Authors: | Steve Kirkland |
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Institution: | (1) Department of Mathematics and Statistics, University of Regina, Regina, Saskatchewan, S4S OA2, Canada |
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Abstract: | A tree is classified as being type I provided that there are two or more Perron branches at its characteristic vertex. The question arises as to how one might construct such a tree in which the Perron branches at the characteristic vertex are not isomorphic. Motivated by an example of Grone and Merris, we produce a large class of such trees, and show how to construct others from them. We also investigate some of the properties of a subclass of these trees. Throughout, we exploit connections between characteristic vertices, algebraic connectivity, and Perron values of certain positive matrices associated with the tree. |
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