On bipartite-mixed graphs

Abstract

Mixed graphs can be seen as digraphs that have both arcs and edges (or digons, that is, two opposite arcs). In this arti- cle, we consider the case where such graphs are bipartite. As main results, we show that in this context the Moore- like bound is attained in the case of diameter k = 3, and that bipartite-mixed graphs of diameter k ≥ 4 do not exist.

This research have been partially supported by AGAUR under project 2017SGR1087 (C. D. and M.A. F.). The author N. L. has been supported in part by grant MTM2013-46949-P, from Ministerio de Economía y Competitividad, Spain.