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Title:
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Constructions of small regular bipartite graphs of girth 6
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Author:
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Araujo Pardo, M. Gabriela; Balbuena Martínez, Maria Camino Teófila
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Other authors:
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Universitat Politècnica de Catalunya. Departament de Matemàtica Aplicada III; Universitat Politècnica de Catalunya. COMBGRAPH - Combinatòria, Teoria de Grafs i Aplicacions |
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Abstract:
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In this article, some structures in the projective plane of order q are found which allow us to construct small k - regular balanced bipartite graphs of girth 6 for all k ≤ q.
When k = q, the order of these q-regular graphs is 2(q^2−1); and when k ≤ q−1, the order of these k -regular graphs is 2(qk − 2). Moreover, the incidence matrix of
a k -regular balanced bipartite graph of girth 6 having 2(qk −2) vertices, where k is an integer and q is a prime power with 3 ≤ k ≤ q − 1, is provided. These graphs improve upon the best known upper bounds for the number of vertices in regular graphs of girth 6. |
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Subject(s):
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-Àrees temàtiques de la UPC::Matemàtiques i estadística::Matemàtica discreta::Teoria de grafs
-Magic squares
-Projective planes
-Bipartite graphs
-Grafs, Teoria de
-Geometria projectiva
-Quadrats màgics |
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Rights:
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Document type:
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Article - Published version
Article |
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