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New results on the degree/diameter problem of mixed Abelian Cayley graphs

2019/08/01 by C. Dalfó, M.A. Fiol, Dalfó, C. +3
Computer Science · Mathematics · #Combinatorics (math.CO) #FOS: Mathematics #Finite Group Theory Research #Graph theory and applications #Interconnection Networks and Systems

paper · pdf · doi:10.48550/arxiv.1908.00245

openalex publication_date 2019/08/01 · openalex created_date 2019/08/13 · openalex updated_date 2026/07/28

Abstract

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 in which such graphs are Cayley graphs of Abelian groups. These groups can be constructed by using a generalization to ℤn of the concept of congruence in ℤ. Here we use this approach to present some families of mixed graphs, which, for every fixed value of the degree, have an asymptotically large number of vertices as the diameter increases. In some cases, the results obtained are shown to be optimal.

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