Work

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

Year: 2024

Type: article

Abstract: An (ir,z,k/i)-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 logsub2/sub iN/i .

Source: Open Research Online (The Open University)