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 ...

Considering a connected graph $G$ with diameter $D$, we say that it is \emph{$k$-walk-regular}, for a given integer $k$ $(0\leq k \leq D)$, if the number of walks of length $\ell$ between vertices $u$ and $v$ only depends ...

In this note we present a general approach to construct large digraphs from small ones. These are called expanded digraphs, and, as particular cases, we show their close relationship between voltage digraphs and line ...

A graph is walk-regular if the number of cycles of length rooted at a given vertex is a constant through all the vertices. For a walk-regular graph G with d+1 different eigenvalues and spectrally maximum diameter D = ...

In this paper we follow the study of the hierarchical product of graphs, an operation recently introduced in the context of networks. A well-known example of such a product is the binomial tree which is the (hierarchical) ...