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 M_h(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]): M_h(r) is nonderogatory if and only if r=2.

Keywords : Nonderogatory matrix; characteristic polynomial of directedgraphs; directed windmills.

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