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

Dalfó, C.; Erskine, G.; Exoo, G.; Fiol, M.A.; López, N.; Messegué, A. and Tuite, J. (2024). On large regular ( 1 , 1 , k ) -mixed graphs. Discrete Applied Mathematics, 356 pp. 209–228.

DOI: https://doi.org/10.1016/j.dam.2024.06.001

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 log₂ N .

Viewing alternatives

Metrics

Item Actions

Export

You can export this page using these formats Digital Object Identifier - DOI