2025/03/21 by Gabriela Araujo‐Pardo, Araujo-Pardo, Gabriela, Lydia Mirabel Mendoza-Cadena +1 · 1 citation
Mathematics · Computer Science · #Finite Group Theory Research #Interconnection Networks and Systems #Graph Labeling and Dimension Problems
paper · pdf · doi:10.48550/arxiv.2503.17152
A mixed regular graph is a graph where every vertex has z incoming arcs, z outgoing arcs, and r edges; furthermore, if it has girth g, we say that the graph is a [z,r;g]-mixed graph. A [z,r;g]-mixed cage is a [z,r;g]-mixed graph with the smallest possible order. In this note, we give a family of [z,q;5]-mixed graphs for q≥ 7 power of prime and q-1≤ 4z+R with z≥ 1 and R ∈ \1,…,5\. This provides better upper bounds on the order of mixed cages until this moment.