It is known that Moore digraphs of degree d and diameter k do not ex ist see or Furthermore for degree it is shown that for k there are no digraphs of order close to i e one less than Moore bound In this paper we shall consider digraphs of diameter k degree and number of vertices one less than Moore bound We give a necessary condition for the existence of such digraphs and using this condition ...

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 CK(d, `) and the subKautz sK(d, 2) digraphs were recently introduced by Böhmová, Huemer and the author. In this paper we propose a new method to obtain the complete spectra of subKautz sK(d, 2) and cyclic Kautz CK(d, 3) digra...

Eternal and m-eternal domination are concerned with using mobile guards to protect a graph against infinite sequences of attacks at vertices. Eternal domination allows one guard to move per attack, whereas more than one guard may move per attack in the m-eternal domination model. Inequality chains consisting of the domination, eternal domination, m-eternal domination, independence, and clique c...

We consider a directed version of Deza graphs. A digraph is said to be a Deza digraph if it is regular and the number of common out-neighbors of any two distinct vertices takes on at most two values. We introduce some constructions and develop some basic theory. In particular, constructions from Cayley digraphs, graph lexicograph products and graph directed products are described. Moreover, we ...

In [19] Huang gave a characterization of local tournaments. His characterization involves arc-reversals and therefore may not be easily used to solve other structural problems on locally semicomplete digraphs (where one deals with a fixed locally semicomplete digraph). In this paper we derive a classification of locally semicomplete digraphs which is very useful for studying structural properti...

In this article, we present a detailed study of the reach distance-layer structure De Bruijn and Kautz digraphs, apply our analysis to performance evaluation deflection routing in networks. Concerning structure, provide explicit polynomial expressions, terms degree digraph, for cardinalities some relevant sets structure. Regarding application defection routing, as consequence description formul...

We call a digraph D = (V,E) a maximal m-free digraph if only if D has no cycles of length at most m and adding any ordered pair (u, v) 6∈ E will create a cycle of length at most m. In this note, we investigate this special class of digraphs. We will show that these digraphs share similar properties with tournament digraphs and this ”maximality” condition can be used to solve several extremal pr...

This paper describes algorithms for answering shortest path queries in digraphs with small separators and, in particular, in planar digraphs. In this version of the problem, one has to preprocess the input graph so that, given an arbitrary pair of query vertices v and w, the shortest-path distance between v and w can be computed in a short time. The goal is to achieve balance between the prepro...

There is increasing interest in the design of dense vertex-symmetric graphs and digraphs as models of interconnection networks for implementing parallelism. In these systems many nodes are connected with relatively few links and short paths between them and each node may execute, without modifications, the same communication software. In this paper we give new families of dense vertex-symmetric...