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Revista Colombiana de Matemáticas
Print version ISSN 0034-7426
Abstract
RADA, JUAN. Nonderogatory directed windmills. Rev.colomb.mat. [online]. 2008, vol.42, n.1, pp.61-66. ISSN 0034-7426.
A directed graph G is nonderogatory if its adjacency matrix A is nonderogatory, i.e., the characteristic polynomial of A is equal to the minimal polynomial of A. Given integers r≥ 2 and h≥ 3, a directed windmill Mh(r) is a directed graph obtained by coalescing r dicycles of length h in one vertex. In this article we solve a conjecture proposed by Gan and Koo ([3]): Mh(r) is nonderogatory if and only if r=2.
Keywords : Nonderogatory matrix; characteristic polynomial of directedgraphs; directed windmills.