It is an elementary exercise to show that any non-trivial simple graph has two vertices with the same degree. This is not the case for digraphs and multigraphs. We consider generating irregular digraphs from arbitrary digraphs by adding multiple arcs. To this end, we define an irregular labeling of a digraph D to be an arc labeling of the digraph such that the ordered pairs of the sums of the i...

An even factor in a digraph is a collection of vertex-disjoint dipaths and even dicycles, which generalizes a path-matching introduced by Cunningham and Geelen (1997). In a restricted class of digraphs, called odd-cycle-symmetric, Pap (2005) presented a combinatorial algorithm to find a maximum even factor. In a certain class of weighted digraphs, called odd-cycle-symmetric, Király and Makai (2...

The p-competition graph G of a digraph D is a graph on the same vertex set as D, with x; y] 2 E(G) if and only if jOut(x) \Out(y)j p in D. In this paper we focus on the case in which D is a symmetric digraph ((a; b) is an arc in D if and only if (b; a) is an arc in D). We relate the problem to 2-step graphs, squares, and a generalization of the neighborhood graph called the p-neighborhood graph...

 It is known that the directed cycle of order $n$ uniquely achieves the minimum spectral radius among all strongly connected digraphs of order $nge 3$. In this paper, among others, we determine the digraphs which achieve the second, the third and the fourth minimum spectral radii respectively among strongly connected digraphs of order $nge 4$.  

two digraphs of same order are said to be skew-equienergetic if theirskew energies are equal. one of the open problems proposed by li andlian was to construct non-cospectral skew-equienergetic digraphs onn vertices. recently this problem was solved by ramane et al. inthis paper, we give some new methods to construct new skew-equienergeticdigraphs.

A ~ P3-decomposition of a directed graph D is a partition of the arcs of D into directed paths of length 2. We characterize symmetric digraphs that do not admit a ~ P3-decomposition. We show that the only 2-regular, connected directed graphs that do not admit a ~ P3-decomposition are obtained from undirected odd cycles by replacing each edge by two oppositely directed arcs. In both cases, we gi...

In this paper we present algorithms for drawing series parallel digraphs with as much symmetry as possible. The first step is to compute a certain kind of automorphism, called an “upward planar automorphism” for an input series parallel digraph. The next step uses these automorphisms to construct a symmetric drawing of the graph. We present several variations of the second step, with visibility...

Cumulants of noncommutative random variables arising from Fock space constructions are considered. In particular, simplified calculations are given for several known examples on q-Fock spaces. In the second half of the paper we consider in detail the Fock states associated to characters of the infinite symmetric group recently constructed by Bożejko and Guta. We express moments of multidimensio...