P2p -factorization of a complete bipartite graph for p, an integer was studied by Wang [1]. Further, Beiling [2] extended the work of Wang[1], and studied the P2k -factorization of complete bipartite multigraphs. For even value of k in Pk -factorization the spectrum problem is completely solved [1, 2, 3]. However for odd value of k i.e. P3 , P5 and P7 , the path factorization have been studied ...

— A new class of generating Systems (the bdg Systems), is introduced and they are shown to be equivalent to the class of programmed grammars. They have independent interest since their définition gives doser ties between language theory and graph theory. This in turn gives rise to a number of interesting hybrid graph — grammar open problems.

— A new class of generating Systems (the bdg Systems), is introduced and they are shown to be equivalent to the class of programmed grammars. They have independent interest since their définition gives doser ties between language theory and graph theory. This in turn gives rise to a number of interesting hybrid graph — grammar open problems.

We consider finite and simple digraphs. Usually, we use G to denote a graph and D to a digraph. Undefined terms and notations will follow [6] for graphs and [3] for digraphs. In particular, κ(G), κ′(G), α(G) ans α′(G) denote the connectivity, the edge connectivity, the independence number, and the matching number of a graph G; and λ(D) denotes the arc-strong connectivity of a digraph D as well ...

A Playfair cipher is a digraph substitution, where each letter pair of the plaintext is replaced by a letter pair in the ciphertext. The chart of substitutions is summarized by the placement of letters in a table, called the Playfair square, constructed in some customary manner from a keyword. We denote a substitution of plaintext digraph cd with ciphertext digraph ab by ab− cd. There are two r...

The Shapley value for directed graph (digraph) games, TU games with limited cooperation introduced by an arbitrary digraph prescribing the dominance relation among the players, is introduced. It is defined as the average of marginal contribution vectors corresponding to all permutations that do not violate the subordination of players. We assume that in order to cooperate players may join only ...

In 1981, Bermond and Thomassen conjectured that every digraph with minimum out-degree at least 2k − 1 contains k disjoint cycles. This conjecture is trivial for k = 1, and was established for k = 2 by Thomassen in 1983. We verify it for the next case, by proving that every digraph with minimum out-degree at least five contains three disjoint cycles. To show this, we improve Thomassen’s result b...

Manoussakis, Y. and D. Amar, Hamiltonian paths and cycles, number of arcs and independence number in digraphs, Discrete Mathematics 105 (1992) 157-172. We let D denote a digraph with n vertices, independence number at least (Y and half-degrees at least k. We give (i) a function f(n, a) (respectively f (n, k, a)) such that any digraph with at least f(n, a) (respectively f(n, k, a)) arcs is Hamil...

LetD = (V,A) be a finite and simple digraph. A Roman dominating function (RDF) on a digraph D is a labeling f : V (D) → {0, 1, 2} such that every vertex with label 0 has a in-neighbor with label 2. The weight of an RDF f is the value ω(f) = ∑ v∈V f(v). The Roman domination number of a digraph D, denoted by γR(D), equals the minimum weight of an RDF on D. In this paper we present some sharp boun...

Let F be a cellular automaton on the space of all sequences from a finite alphabet. From the local description of F a finite labeled digraph is constructed with a distinguished subdi graph. The surjectivity and openness of F are proved to correspond to properties of these digraphs. Similarly, another finite labeled digraph is constructed with a distin guished subset of its vert ex set . Th e in...