3er. 2010
This edition of IWONT is dedicated to Professor Miquel Àngel Fiol on the occasion of his 60th birthday
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Proceedings of the 3rd International Workshop on Optimal Networks Topologies IWONT 2010
(201102)
Conference lecture
Open Access 
The beginnings
(2011)
Conference report
Open AccessThe simple title tells many things. Of course, it could tell almost nothing since a wellknown motto says that ‘everything must have a beginning’. However, another motto is more appropriate here: ‘A journey of a thousand ... 
Infinite families of 3numerical semigroups with arithmeticlike links
(2011)
Conference report
Open AccessLet 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 ... 
On identifying codes in partial linear spaces
(2011)
Conference report
Open AccessLet (P,L, I) be a partial linear space and X ⊆ P ∪ L. Let us denote by (X)I = x∈X{y : yIx} and by [X] = (X)I ∪ X. With this terminology a partial linear space (P,L, I) is said to admit a (1,≤ k)identifying code if the ... 
Subdivisions in a bipartite graph
(2011)
Conference report
Open AccessGiven 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 ... 
On the λ'optimality of sgeodetic digraphs
(2011)
Conference report
Open AccessFor a strongly connected digraph D the restricted arcconnectivity λ'(D) is defined as the minimum cardinality of an arccut over all arccuts S satisfying that D − S has a non trivial strong component D1 such that D − V ... 
On the connectivity and restricted edgeconnectivity of 3arc graphs
(2011)
Conference report
Open AccessA 3−arc of a graph G is a 4tuple (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 3arc graph X(G) of a given graph G is ... 
Edgesuperconnectivity of semiregular cages with odd girth
(2011)
Conference report
Open AccessA graph is said to be edgesuperconnected if each minimum edgecut consists of all the edges incident with some vertex of minimum degree. A graph G is said to be a {d, d + 1} semiregular graph if all its vertices have ... 
MMatrix Inverse problem for distanceregular graphs
(2011)
Conference report
Open AccessWe 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 MoorePenrose inverse of the ... 
Graphs with equal domination and 2domination numbers
(2011)
Conference report
Open AccessFor a graph G a subset D of the vertex set of G is a kdominating set if every vertex not in D has at least k neighbors in D. The kdomination number γk(G) is the minimum cardinality among the kdominating sets of G. Note ... 
Spectral behavior of some graph and digraph compositions
(2011)
Conference report
Open AccessLet 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 ... 
On the existence of combinatorial configurations
(2011)
Conference report
Open AccessA (v, b, r, k) combinatorial configuration can be defined as a connected, (r, k)biregular bipartite graph with v vertices on one side and b vertices on the other and with no cycle of length 4. Combinatorial configurations ... 
Symmetric Lgraphs
(2011)
Conference report
Open AccessIn this paper we characterize symmetric Lgraphs, 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 ... 
On the vulnerability of some families of graphs
(2011)
Conference report
Open AccessThe toughness of a noncomplete graph G is defined as τ (G) = min{S/ω(G − S)}, where the minimum is taken over all cutsets S of vertices of G and ω(G − S) denotes the number of components of the resultant graph G − S by ... 
On the diameter of random planar graphs
(2011)
Conference report
Open AccessWe 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{} ... 
Radially Moore graphs of radius three and large odd degree
(2011)
Conference report
Open AccessExtremal graphs which are close related to Moore graphs have been defined in different ways. Radially Moore graphs are one of these examples of extremal graphs. Although it is proved that radially Moore graphs exist for ... 
Application layer multicast algorithm
(2011)
Conference report
Open AccessThis paper presents a multicast algorithm, called MSMs, for pointtomultipoint 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 ... 
On the krestricted edgeconnectivity of matched sum graphs
(2011)
Conference report
Open AccessA matched sum graph $G_1$M$G_2$ of two graphs $G_1$ and $G_2$ of the same order n is obtained by adding to the union (or sum) of $G_1$ and $G_2$ a set M of n independent edges which join vertices in V ($G_1$) to vertices ... 
An overview of the degree/diameter problem for directed, undirected and mixed graphs
(2011)
Conference report
Open AccessA wellknown 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, ... 
Large graphs of diameter two and given degree
(2011)
Conference report
Open AccessLet r(d, 2), C(d, 2), and AC(d, 2) be the largest order of a regular graph, a Cayley graph, and a Cayley graph of an Abelian group, respectively, of diameter 2 and degree d. The best currently known lower bounds on these ... 
Fiedler’s Clustering on mdimensional Lattice Graphs
(2011)
Conference report
Open AccessWe consider the partitioning of mdimensional 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 ... 
Large digraphs of given diameter and degree from coverings
(2011)
Conference report
Open AccessWe show that a construction of Comellas and Fiol for large vertextransitive digraphs of given degree and diameter from small digraphs preserves the properties of being a Cayley digraph and being a regular covering. 
Dual concepts of almost distanceregularity and the spectral excess theorem
(2011)
Conference report
Open AccessGenerally speaking, ‘almost distanceregular’ graphs are graphs that share some, but not necessarily all, regularity properties that characterize distanceregular graphs. In this paper we first propose two dual concepts ... 
Large Edgenonvulnerable Graphs
(2011)
Conference report
Open AccessIn this paper we study the graphs such that the deletion of any edge does not increase the diameter. We give some upper bounds for the order of such a graph with given maximum degree and diameter. On the other hand ... 
A mathematical model for dynamic memory networks
(2011)
Conference report
Open AccessThe 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 ... 
Algebraic characterizations of bipartite distanceregular graphs
(2011)
Conference report
Open AccessBipartite graphs are combinatorial objects bearing some interesting symmetries. Thus, their spectra—eigenvalues of its adjacency matrix—are symmetric about zero, as the corresponding eigenvectors come into pairs. Moreover, ... 
Topology of Cayley graphs applied to inverse additive problems
(2011)
Conference report
Open AccessWe 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 ≤ ...