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arXiv · 2306.04521

On large regular (1,1,k)-mixed graphs

C. Dalfó·G. Erskine·G. Exoo·M. A. Fiol·N. López·A. Messegué·J. Tuite
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Abstract

An $(r,z,k)$-mixed graph $G$ has every vertex with undirected degree $r$, directed in- and out-degree $z$, and diameter $k$. In this paper, we study the case $r=z=1$, proposing some new constructions of $(1,1,k)$-mixed graphs with a large number of vertices $N$. Our study is based on computer techniques for small values of $k$ and the use of graphs on alphabets for general $k$. In the former case, the constructions are either Cayley or lift graphs. In the latter case, some infinite families of $(1,1,k)$-mixed graphs are proposed with diameter of the order of $2\log_2 N$.

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C. Dalfó, G. Erskine, G. Exoo, M. A. Fiol, N. López, A. Messegué, J. Tuite. 2023-06-07. On large regular (1,1,k)-mixed graphs. https://arxiv.org/abs/2306.04521

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