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Opis: Mixed graphs can be seen as digraphs that have both arcs and edges (or digons, that is, two opposite arcs). In this paper, we consider the case where such graphs are bipartite and in which the undirected and directed degrees are one. The best graphs, in terms of the number of vertices, are presented for small diameters. Moreover, two infinite families of such graphs with diameter k and number of vertices of the order of 2k/2 are proposed, one of them being totally regular (1,1)-mixed graphs. In addition, we present two more infinite families called chordal ring and chordal double ring mixed graphs, which are bipartite and related to tessellations of the plane. Finally, we give an upper bound that improves the Moore bound for bipartite mixed graphs for r = z = 1.
Ključne besede: mixed graph, degree/diameter problem, Moore bound, bipartite graph
Objavljeno v RUP: 03.11.2025; Ogledov: 108; Prenosov: 0
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Opis: An infinite series and some sporadic examples of large Cayley graphs with given degree and diameter are constructed. The graphs arise from arcs, caps and other objects of finite projective spaces.
Ključne besede: degree, diameter problem, Moore bound, finite projective spaces
Objavljeno v RUP: 15.10.2013; Ogledov: 17597; Prenosov: 80
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