Generalized exponents of primitive symmetric digraphs
نویسندگان
چکیده
منابع مشابه
Generalized Exponents of Primitive Symmetric Digraphs
A strongly connected digraph D of order n is primitive (aperiodic) provided the greatest common divisor of its directed cycle lengths equals 1. For such a digraph there is a minimum integer t, called the exponent of D, such that given any ordered pair of vertices x and y there is a directed walk from x to y of length t. The exponent of D is the largest of n ‘generalized exponents’ that may be a...
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A digraph G = (V; E) is primitive if, for some positive integer k, there is a u ! v walk of length k for every pair u; v of vertices of V. The minimum such k is called the exponent of G, denoted exp(G). The local exponent of G at a vertex u 2 V , denoted exp G (u), is the least integer k such that there is a u ! v walk of length k for each v 2 V. Let V = f1; 2; ; ng. Following Brualdi and Liu, ...
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متن کاملGeneralized exponents of non-primitive graphs
The exponent of a primitive digraph is the smallest integer k such that for each ordered pair of (not necessarily distinct) vertices x and y there is a walk of length k from x to y. As a generalization of exponent, Brualdi and Liu (Linear Algebra Appl. 14 (1990) 483499) introduced three types of generalized exponents for primitive digraphs in 1990. In this Paper we extend their definitions of g...
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ژورنال
عنوان ژورنال: Discrete Applied Mathematics
سال: 1997
ISSN: 0166-218X
DOI: 10.1016/s0166-218x(96)00077-7