The notion of a C-ultrahomogeneous (or C-UH) graph due to D. Isaksen et al. is adapted for digraphs and applied to the cubic distance-transitive graphs considered both as graphs and digraphs when C is formed by shortest cycles and (k − 1)-paths with k = arc-transitivity. Moreover, (k − 1)powers of shortest cycles taken with orientation assignments that make these graphs become C-UH digraphs are...

Computing short regular expressions equivalent to a given finite automaton is a hard task. In this work we present a class of acyclic automata for which it is possible to obtain in time O(n2 log n) an equivalent regular expression of size O(n). A characterisation of this class is made using properties of the underlying digraphs that correspond to the series-parallel digraphs class. Using this c...

A dicycle cover of a digraphD is a familyF of dicycles ofD such that each arc ofD lies in at least one dicycle inF. We investigate the problem of determining the upper bounds for the minimum number of dicycles which cover all arcs in a strong digraph. Best possible upper bounds of dicycle covers are obtained in a number of classes of digraphs including strong tournaments, Hamiltonian oriented g...

A digraph is odd-cycle-symmetric if every arc in any elementary odd directed cycle has the reverse arc. This concept arises in the context of the even factor problems, which generalize the path-matching problems. While the even factor problem is NP-hard in general digraphs, it is solvable in polynomial time for odd-cycle-symmetric digraphs. This paper provides a characterization of odd-cycle-sy...

The exponent of a primitive digraph is the smallest integer k such that for each ordered pair of (not necessarily distinct) vertices x and y there is a walk of length k from x to y. As a generalization of exponent, Brualdi and Liu (Linear Algebra Appl. 14 (1990) 483499) introduced three types of generalized exponents for primitive digraphs in 1990. In this Paper we extend their definitions of g...

In the Directed k-Chinese Postman Problem (k-DCPP), we are given a connected weighted digraph G and asked to find k non-empty closed directed walks covering all arcs of G such that the total weight of the walks is minimum. Gutin, Muciaccia and Yeo (Theor. Comput. Sci. 513 (2013) 124–128) asked for the parameterized complexity of k-DCPP when k is the parameter. We prove that the k-DCPP is fixed-...

If D = (V,A) is a digraph, its competition hypergraph CH(D) has vertex set V and e ⊆ V is an edge of CH(D) iff |e| ≥ 2 and there is a vertex v ∈ V , such that e = N− D (v) = {w ∈ V |(w, v) ∈ A}. We give characterizations of CH(D) in case of hamiltonian digraphs D and, more general, of digraphs D having a τ -cycle factor. The results are closely related to the corresponding investigations for co...

Many problems of practical interest can be modeled and solved by using graph algorithms. In general, graph theory has a wide range of applications in diverse fields. In this paper, the intuitionistic fuzzy organizational and neural network models, intuitionistic fuzzy neurons in medical diagnosis, intuitionistic fuzzy digraphs in vulnerability assessment of gas pipeline networks, and intuitioni...