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This edition of IWONT is dedicated to Professor Miquel Àngel Fiol on the occasion of his 60th birthday

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Ara es mostren els items 1-27 de 27

• #### Proceedings of the 3rd International Workshop on Optimal Networks Topologies IWONT 2010 ﻿

(2011-02)
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• #### The beginnings ﻿

(2011)
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The simple title tells many things. Of course, it could tell almost nothing since a well-known motto says that ‘everything must have a beginning’. However, another motto is more appropriate here: ‘A journey of a thousand ...
• #### Infinite families of 3-numerical semigroups with arithmetic-like links ﻿

(2011)
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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 ...
• #### On identifying codes in partial linear spaces ﻿

(2011)
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Let (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)
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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 ...
• #### On the λ'-optimality of s-geodetic digraphs ﻿

(2011)
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For a strongly connected digraph D the restricted arc-connectivity λ'(D) is defined as the minimum cardinality of an arc-cut over all arc-cuts S satisfying that D − S has a non trivial strong component D1 such that D − V ...
• #### On the connectivity and restricted edge-connectivity of 3-arc graphs ﻿

(2011)
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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 ...
• #### Edge-superconnectivity of semiregular cages with odd girth ﻿

(2011)
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A graph is said to be edge-superconnected if each minimum edge-cut 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 ...
• #### M-Matrix Inverse problem for distance-regular graphs ﻿

(2011)
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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 ...
• #### Graphs with equal domination and 2-domination numbers ﻿

(2011)
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For a graph G a subset D of the vertex set of G is a k-dominating set if every vertex not in D has at least k neighbors in D. The k-domination number γk(G) is the minimum cardinality among the k-dominating sets of G. Note ...
• #### Spectral behavior of some graph and digraph compositions ﻿

(2011)
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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 ...
• #### On the existence of combinatorial configurations ﻿

(2011)
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A (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 L-graphs ﻿

(2011)
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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 ...
• #### On the vulnerability of some families of graphs ﻿

(2011)
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The 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)
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• #### An overview of the degree/diameter problem for directed, undirected and mixed graphs ﻿

(2011)
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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, ...
• #### Large graphs of diameter two and given degree ﻿

(2011)
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Let 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 m-dimensional Lattice Graphs ﻿

(2011)
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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 ...
• #### Large digraphs of given diameter and degree from coverings ﻿

(2011)
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We show that a construction of Comellas and Fiol for large vertex-transitive 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 distance-regularity and the spectral excess theorem ﻿

(2011)
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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 ...
• #### Large Edge-non-vulnerable Graphs ﻿

(2011)
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In 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)
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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 ...
• #### Algebraic characterizations of bipartite distance-regular graphs ﻿

(2011)
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Bipartite 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)
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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| ≤ ...