Smooth digraphs modulo primitive positive constructability and cyclic loop conditions

The m-competition indices of symmetric primitive digraphs with loop

Well primitive digraphs

A primitive digraph D is said to be well primitive if the local exponents of D are all equal. In this paper we consider well primitive digraphs of two special types: digraphs that contain loops, and symmetric digraphs with shortest odd cycle of length r. We show that the upper bound of the exponent of the well primitive digraph is n− 1 in both these classes of digraphs, and we characterize the ...

Loop Detection in Prolog by Searching for Primitive Cyclic Goals

A new method will be proposed for the detection of some loops during depth-first search in Prolog, and an implementation of this method will be described. The method is a modification of another one presented in the paper [3]. As in [3], we shall consider only Prolog programs consisting of Horn clauses and goals consisting of atomic formulas. The new method has the following advantage: only the...

Local Exponents of Primitive Digraphs

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, ...

From subKautz digraphs to cyclic Kautz digraphs

Kautz digraphs K(d, `) are a well-known family of dense digraphs, widely studied as a good model for interconnection networks. Closely related with these, the cyclic Kautz digraphs CK(d, `) were recently introduced by Böhmová, Huemer and the author, and some of its distance-related parameters were fixed. In this paper we propose a new approach to cyclic Kautz digraphs by introducing the family ...