Revista Colombiana de Matemáticas
versión impresa ISSN 0034-7426
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 (): Mh(r) is nonderogatory if and only if r=2.
Palabras llave : Nonderogatory matrix; characteristic polynomial of directedgraphs; directed windmills.