On (4, 2)-digraphs containing a cycle of length 2.
On a certain class of multidigraphs, for which reversal of no arc decreases the number of their cycles
On a certain numbering of the vertices of a hypergraph
On a classification of Hamiltonian tournaments
On a conjecture by Nash-Williams
On a conjecture of quintas and arc-traceability in upset tournaments
A digraph D = (V,A) is arc-traceable if for each arc xy in A, xy lies on a directed path containing all the vertices of V, i.e., hamiltonian path. We prove a conjecture of Quintas [7]: if D is arc-traceable, then the condensation of D is a directed path. We show that the converse of this conjecture is false by providing an example of an upset tournament which is not arc-traceable. We then give a characterization for upset tournaments in terms of their score sequences, characterize which arcs of...
On a conjecture of the semigroup of fully indecomposable relations
On a connection of number theory with graph theory
We assign to each positive integer a digraph whose set of vertices is and for which there is a directed edge from to if . We establish necessary and sufficient conditions for the existence of isolated fixed points. We also examine when the digraph is semiregular. Moreover, we present simple conditions for the number of components and length of cycles. Two new necessary and sufficient conditions for the compositeness of Fermat numbers are also introduced.
On a problem of E. Prisner concerning the biclique operator
The symbol denotes a directed graph with the vertex set for two (not necessarily disjoint) vertex sets in which an arc goes from each vertex of into each vertex of . A subdigraph of a digraph which has this form is called a bisimplex in . A biclique in is a bisimplex in which is not a proper subgraph of any other and in which and . The biclique digraph of is the digraph whose vertex set is the set of all bicliques in and in which there is an arc from into if and only...
On a problem of walks
In 1995, F. Jaeger and M.-C. Heydemann began to work on a conjecture on binary operations which are related to homomorphisms of De Bruijn digraphs. For this, they have considered the class of digraphs such that for any integer , has exactly walks of length , where is the order of . Recently, C. Delorme has obtained some results on the original conjecture. The aim of this paper is to recall the conjecture and to report where all the authors arrived.
On Arbitrarily Traceable Graphs.
On automorphisms of digraphs without symmetric cycles
A digraph is a symmetric cycle if it is symmetric and its underlying graph is a cycle. It is proved that if is an asymmetric digraph not containing a symmetric cycle, then remains asymmetric after removing some vertex. It is also showed that each digraph without a symmetric cycle, whose underlying graph is connected, contains a vertex which is a common fixed point of all automorphisms of .
On Certain Classes of rigid groups
On Complex Eigenvalues of M and P Matrices.
On Cycles in Tournaments
On -algebras
On digraphs with non-derogatory adjacency matrix.
On directed triangles in digraphs.
On expansions and extensions of powerful digraphs.
On factorization of probability distributions over directed graphs
Four notions of factorizability over arbitrary directed graphs are examined. For acyclic graphs they coincide and are identical with the usual factorization of probability distributions in Markov models. Relations between the factorizations over circuits are described in detail including nontrivial counterexamples. Restrictions on the cardinality of state spaces cause that a factorizability with respect to some special cyclic graphs implies the factorizability with respect to their, more simple,...