منابع مشابه
Research Article Nonderogatory Unicyclic Digraphs
A digraph is nonderogatory if its characteristic polynomial and minimal polynomial are equal. Relations between nonderogatory digraphs and their automorphism groups have appeared in the literature (see [1] and [2, Theorem 5.10]). More recently, several articles (see, e.g., [1, 3–8]) address the problem of determining when certain operations between nonderogatory digraphs are again nonderogatory...
متن کاملNonderogatory Directed Webgraph
Let G be a digraph with vertices labelled {1, 2, . . . , n} and its adjacency matrix A(G) the n × n matrix whose ijth entry is the number of arcs joining vertex i to vertex j. A digraph is nonderogatory if the characteristic polynomial and minimal polynomial of its adjacency matrix are equal. Computation of the minimal polynomial of a matrix is harder than the characteristic polynomial especial...
متن کاملMore skew-equienergetic digraphs
Two digraphs of same order are said to be skew-equienergetic if their skew energies are equal. One of the open problems proposed by Li and Lian was to construct non-cospectral skew-equienergetic digraphs on n vertices. Recently this problem was solved by Ramane et al. In this paper, we give some new methods to construct new skew-equienergetic digraphs.
متن کاملOn Unicyclic Reflexive Graphs
If G is a simple graph (a non-oriented graph without loops or multiple edges), its (0, 1)-adjacency matrix A is symmetric and roots of the characteristic polynomial PG (λ) = det (λI −A) (the eigenvalues of G, making up its spectrum) are all real numbers, for which we assume their non-increasing order: λ1 ≥ λ2 ≥ · · · ≥ λn. In a connected graph for the largest eigenvalue λ1 (the index of the gra...
متن کاملNonderogatory directed windmills Molinos de viento dirigidos no derogatorios
Abstract. 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 nonder...
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ژورنال
عنوان ژورنال: International Journal of Mathematics and Mathematical Sciences
سال: 2007
ISSN: 0161-1712,1687-0425
DOI: 10.1155/2007/46851