By using biclique partitions of digraphs, this paper gives reduction formulas for the number oriented spanning trees, stationary distribution vector and Kemeny's constant digraphs. As applications, we give a method enumerating trees undirected graphs by vertex degrees partitions. The partition formula also extends results Knuth Levine from line digraphs to general

Two problems of Cameron, Praeger, and Wormald [Infinite highly arc transitive digraphs and universal covering digraphs, Combinatorica (1993)] are resolved. First, locally finite highly arc-transitive digraphs with universal reachability relation are presented. Second, constructions of two-ended highly arc-transitive digraphs are provided, where each ‘building block’ is a finite bipartite digrap...

We use an exhaustive generation with isomorph-rejection to classify three types of structured digraphs. The first type is the class of regular digraphs where each vertex has the same number of out-neighbors and inneighbors. The second type is the class of normally regular digraphs introduced by Jørgensen. In these digraphs, the number of common out-neighbors (or inneighbors) of vertices x and y...

Containment and overlap representations of digraphs are studied, with the following results. The interval containment digraphs are the digraphs of Ferrers dimension 2, and the circular-arc containment digraphs are the complements of circular-arc intersection digraphs. A poset is an interval containment poset if and only if its comparability digraph is an interval containment digraph, and a grap...

We consider digraphs – called extended locally semicomplete digraphs, or extended LSD’s, for short – that can be obtained from locally semicomplete digraphs by substituting independent sets for vertices. We characterize Hamiltonian extended LSD’s as well as extended LSD’s containing Hamiltonian paths. These results as well as some additional ones imply polynomial algorithms for finding a longes...

The Moore bound for a diregular digraph of degree d and diameter k is Md k d d It is known that digraphs of order Md k do not exist for d and k or In this paper we study digraphs of degree d diameter k and order Md k denoted by d k digraphs Miller and Fris showed that k digraphs do not exist for k Subsequently we gave a necessary condition of the existence of k digraphs namely k digraphs do not...

This work deals with the domination numbers of generalized de Bruijn digraphs and generalized Kautz digraphs. Dominating sets for digraphs are not familiar compared with dominating sets for undirected graphs. Whereas dominating sets for digraphs have more applications than those for undirected graphs. We construct dominating sets of generalized de Bruijn digraphs where obtained dominating sets ...

Abstract. Many “good” topologies for interconnection networks are based on line digraphs of regular digraphs. These digraphs support unitary matrices. We propose the property “being the digraph of a unitary matrix” as additional criterion for the design of new interconnection networks. We define a composition of digraphs, which we call diagonal union. Diagonal union can be used to construct dig...

Berge’s elegant strong path partition conjecture from 1982 extends the Greene-Kleitman Theorem and Dilworth’s Theorem for all digraphs. The conjecture is known to be true for all digraphs for k = 1 by the Gallai-Milgram Theorem, and for k > 1 only for acyclic digraphs. We present a simple algorithmic proof for k = 1 which naturally extends to a new algorithmic proof for acyclic digraphs for all...

In this note we present a general approach to construct large digraphs from small ones. These are called expanded digraphs, and, as particular cases, we show the close relationship between lifted digraphs of voltage digraphs and line digraphs, which are two known ways to obtain dense digraphs. In the same context, we show the equivalence between the vertex-splitting and partial line digraph tec...