Browsing Articles publicats (Matemàtica) by Author "Araujo Pardo, Martha Gabriela"
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- ItemOpen AccessBipartite biregular Moore graphs(Elsevier, 2021) Araujo Pardo, Martha Gabriela; Dalfó, Cristina; Fiol Mora, Miguel Ángel; López Lorenzo, IgnacioA bipartite graph G=(V,E) with V=V1 U V2 is biregular if all the vertices of a stable set Vi have the same degree ri for i=1,2. In this paper, we give an improved new Moore bound for an infinite family of such graphs with odd diameter. This problem was introduced in 1983 by Yebra, Fiol, and Fàbrega. Besides, we propose some constructions of bipartite biregular graphs with diameter d and large number of vertices N(r1,r2;d), together with their spectra. In some cases of diameters d=3, 4, and 5, the new graphs attaining the Moore bound are unique up to isomorphism.
- ItemOpen AccessOn New Record Graphs Close to Bipartite Moore Graphs(Springer Nature, 2022) Araujo Pardo, Martha Gabriela; López Lorenzo, IgnacioThe modelling of interconnection networks by graphs motivated the study of several extremal problems that involve well known parameters of a graph (degree, diameter, girth and order) and optimising one of the parameters given restrictions on some of the others. Here we focus on bipartite Moore graphs, that is, bipartite graphs attaining the optimum order, fixed either the degree/diameter or degree/girth. The fact that there are very few bipartite Moore graphs suggests the relaxation of some of the constraints implied by the bipartite Moore bound. First we deal with local bipartite Moore graphs. We find in some cases those local bipartite Moore graphs with local girths as close as possible to the local girths given by a bipartite Moore graph. Second, we construct a family of (q+2)-bipartite graphs of order 2(q2+q+5) and diameter 3, for q a power of prime. These graphs attain the record value for q=9 and improve the values for q=11 and q=13.