Let S = a, b,N be a numerical semigroup generated by a, b,N ∈ N with 1 < a < b < N and gcd(a, b,N) = 1. The conductor of S, denoted by c(S) or c(a, b,N), is the minimum element of S such that c(S) + m ∈ S for all m ∈ N ...

Given a bipartite graph G with m and n vertices, respectively,in its vertices classes, and given two integers s, t such that 2 ≤ s ≤ t, 0 ≤ m−s ≤ n−t, and m+n ≤ 2s+t−1, we prove that if G has at least mn−(2(m−s)+n−t) edges ...

A 3−arc of a graph G is a 4-tuple (y, a, b, x) of vertices such that both (y, a, b) and (a, b, x) are paths of length two in G. Let ←→G denote the symmetric digraph of a graph G. The 3-arc graph X(G) of a given graph G is ...

We analyze when the Moore–Penrose inverse of the combinatorial Laplacian of a distance–regular graph is a M–matrix;that is, it has non–positive off–diagonal elements or, equivalently when the Moore-Penrose inverse of the ...

Let G be a graph of order n the vertices of which are labeled from 1 to n and let $G_1$, · · · ,$G_n$ be n graphs. The graph composition G[$G_1$, · · · ,$G_n$] is the graph obtained by replacing the vertex i of G by the ...

In this paper we characterize symmetric L-graphs, which are either Kronecker products of two cycles or Gaussian graphs. Vertex symmetric networks have the property that the communication load is uniformly distributed on ...

We show that the diameter D(Gn) of a random labelled connected planar graph with n vertices is asymptotically almost surely of order $n^{1/4}$, in the sense that there exists a constant c > 0 such that $P(D(G_n) \in{} ...

This paper presents a multicast algorithm, called MSM-s, for point-to-multipoint transmissions. The algorithm, which has complexity O(n2) in respect of the number n of nodes, is easy to implement and can actually be applied ...

A well-known fundamental problem in extremal graph theory is the degree/diameter problem, which is to determine the largest (in terms of the number of vertices) graphs or digraphs or mixed graphs of given maximum degree, ...

We consider the partitioning of m-dimensional lattice graphs using Fiedler’s approach [1], that requires the determination of the eigenvector belonging to the second smallest eigenvalue of the Laplacian. We examine the ...

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 ...

The aim of this paper is to bring together the work done several years ago by M.A. Fiol and the other authors to formulate a quite general mathematical model for a kind of permutation networks known as dynamic memories. A ...

We present the basic isopermetric structure theory, obtaining some new simplified proofs. Let 1 ≤ r ≤ k be integers. As an application, we obtain simple descriptions for the subsets S of an abelian group with |kS| ≤ ...