We study digraphs preserved by a Maltsev operation: Maltsev digraphs. We show that these digraphs retract either onto a directed path or to the disjoint union of directed cycles, showing in this way that the constraint satisfaction problem for Maltsev digraphs is in logspace, L. We then generalize results from Kazda (2011) to show that a Maltsev digraph is preserved not only by a majority opera...

let $d$ be a digraph with skew-adjacency matrix $s(d)$. then the skew energyof $d$ is defined to be the sum of the norms of all eigenvalues of $s(d)$. denote by$mathcal{o}_n$ the class of digraphs on order $n$ with no even cycles, and by$mathcal{o}_{n,m}$ the class of digraphs in $mathcal{o}_n$ with $m$ arcs.in this paper, we first give the minimal skew energy digraphs in$mathcal{o}_n$ and $mat...

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

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...

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...