Showing papers by "Steve Kirkland published in 1999"
TL;DR: In this article, the question of how to construct a tree in which the Perron branches at the characteristic vertex are not isomorphic is addressed, motivated by an example of Grone and Merris.
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.
8 citations
TL;DR: In this paper, the Kendall Wei method for ranking players in a round robin competition was studied for the class of n × n tournament matrices having a perron vector [1 1 2 3, n − 4 n − 3 n − 2 n − 1]1.