Geodesic
Constructions for type I trees with nonisomorphic Perron branches
Czechoslovak Mathematical Journal, Tome 49 (1999) no. 3, pp. 617-632.

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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.
Classification : 05C05, 05C50, 15A09 
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     author = {Kirkland, Steve},
     title = {Constructions for type {I} trees with nonisomorphic {Perron} branches},
     journal = {Czechoslovak Mathematical Journal},
     pages = {617--632},
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     volume = {49},
     number = {3},
     year = {1999},
     mrnumber = {1708342},
     zbl = {1003.05070},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/CMJ_1999__49_3_a12/}
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Kirkland, Steve. Constructions for type I trees with nonisomorphic Perron branches. Czechoslovak Mathematical Journal, Tome 49 (1999) no. 3, pp. 617-632. http://geodesic.mathdoc.fr/item/CMJ_1999__49_3_a12/