Regular and distance-regular characterizations of general graphs are well-known. In particular, the spectral excess theorem states that a connected graph GG is distance-regular if and only if its spectral excess (a number ...

We present a new matrix-based approach to detect and correct gross errors in GPS geodetic control networks. The study is carried out by introducing a new matrix, whose entries are powers of a (real or complex) variable, ...

A mixed graph G can contain both (undirected) edges and arcs (directed edges). Here we derive an improved Moore-like bound for the maximum number of vertices of a mixed graph with diameter at least three. Moreover, a ...

Given a digraph G, we propose a new method to find the recurrence equation for the number of vertices n_k of the k-iterated line digraph L_k(G), for k>= 0, where L_0(G) = G. We obtain this result by using the minimal polynomial ...

A -identifying code in digraph D is a dominating subset C of vertices of D, such that all distinct subsets of vertices of D with cardinality at most l have distinct closed in-neighborhoods within C. As far as we know, it ...

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 $i\in [0,\ell]$ ...

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 recently been shown that many networks associated with complex systems are small-world (they have both a large local clustering and a small average distance and diameter) and they are also scale-free (the degrees ...

Generally speaking, ‘almost distance-regular’ graphs are graphs that share some, but not necessarily all, regularity properties that characterize distance-regular graphs. In this paper we first propose two dual concepts ...