Kautz digraphs K(d,l) are a well-known family of dense digraphs, widely studied as a good model for interconnection networks. Closely related with these, the cyclic Kautz digraphs CK(d,l) were recently introduced by Böhmová, ...

Com és ben sabut, un graf no dirigit és un objecte matemàtic que modelitza l’existència d’una certa relació entre parells d’elements d’un conjunt donat. Aleshores, no és gaire sorprenent que, al començament, molts dels ...

As is well known, a graph is a mathematical object modeling the existence of a certain relation between pairs of elements of a given set. Therefore, it is not surprising that many of the first results concerning graphs ...

Given an integer ` = 1, a (1, = `)-identifying code in a digraph is a dominating subset C of vertices such that all distinct subsets of vertices of cardinality at most ` have distinct closed in-neighbourhood within C. In ...

Let G be a connected graph with vertex set V and a weight function that assigns a nonnegative number to each of its vertices. Then, the -moment of G at vertex u is de ned to be M G(u) = P v2V (v) dist(u; v), where ...

We obtain a new family of digraphs with minimal diameter, that is, given the number of vertices and out-degree, there is no other digraph with a smaller diameter. This new family of digraphs are called `modified cyclic ...

The Mondrian problem consists of dissecting a square of side length into non-congruent rectangles with natural length sides such that the difference between the largest and the smallest areas of the rectangles partitioning ...

Distance-regular graphs are a key concept in Algebraic Combinatorics and have given rise to several generalizations, such as association schemes. Motivated by spectral and other algebraic characterizations of distance-regular ...

A prominent problem in Graph Theory is to find extremal graphs or digraphs with restrictions in their diameter, degree and number of vertices. Here we obtain a new family of digraphs with minimal diameter, that is, given ...