On bipartite mixed graphs

TL;DR

This paper investigates bipartite mixed graphs, establishing the Moore-like bound for diameter 3 and proving non-existence for diameters 4 and above, advancing understanding of their structural limits.

Contribution

It introduces new bounds for bipartite mixed graphs and proves the non-existence of certain diameters, filling gaps in graph theory knowledge.

Findings

Moore-like bound attained at diameter 3

Bipartite mixed graphs of diameter ≥ 4 do not exist

Provides structural insights into 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 paper, 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 $k\ge 4$ do not exist.