Let G be a (simple) graph with maximum degree three and chromatic index four. A 3-edge-coloring of G is a coloring of its edges in which only three colors are used. Then a vertex is conflicting when some edges incident to ...

Los grafos distancia-regulares aparecen a menudo en el estudio de es- tructuras matemáticas con un alto grado de simetría y/o regularidad. Un ejemplo bien conocido de tales grafos son los esqueletos ...

A graph $\G$ with diameter $D$ and $d+1$ distinct eigenvalues is said to be {\it $(\ell,m)$-walk-regular}, for some integers $\ell\in[0,d]$ and $m\in[0,D]$, $\ell\ge m$, if the number of walks of length $i\in [0,\ell]$ ...

From a natural generalization to Z2 of the concept of congruence, it is possible to define a family of 2-regular digraphs that we call commutative-step networks. Particular examples of such digraphs are the cartesian product ...

Given a simple connected graph $\Gamma$ and a subset of its vertices $C$, the pseudo-distance-regularity around $C$ generalizes, for not necessarily regular graphs, the notion of completely regular code. Up to now, most ...

Connectivity is one of the central concepts of graph theory, from both a theoret- ical and a practical point of view. Its theoretical implications are mainly based on the existence of nice max-min characterization results, ...

A digraph Gamma = (V, E) is a line digraph when every pair of vertices u, v is an element of V have either equal or disjoint in -neighborhoods. When this condition only applies for vertices in a given subset (with at least ...

It has been shown that many networks associated with complex systems are small-world (they have both a large local clustering coefficient and a small diameter) and also scale-free (the degrees are distributed according ...

We introduce the concept of distance mean-regular graph, which can be seen as a generalization of both vertex-transitive and distance-regular graphs. Let G be a graph with vertex set V , diameter D, adjacency matrix A, and ...