2013/01/14 by Sanming Zhou
Computer Science · Engineering · Mathematics · #1-planar graph #Chordal graph #Coding theory and cryptography #Combinatorics #Discrete mathematics #Finite Group Theory Research #Graph #Mathematics #Odd graph #Transitive relation #Unitary state #graph theory and CDMA systems #math.CO #msc:05C25 #msc:05C35
paper · pdf · doi:10.1002/jgt.21721
published as J. Graph Theory 75 (2014), 37-47
openalex publication_date 2013/01/14 · arxiv created 2015/03/24 · arxiv updated 2015/03/25 · openalex created_date 2016/06/24 · openalex updated_date 2026/08/05
Unitary graphs are arc-transitive graphs with vertices the flags of Hermitian unitals and edges defined by certain elements of the underlying finite fields. They played a significant role in a recent classification of a class of arc-transitive graphs that admit an automorphism group acting imprimitively on the vertices. In this article, we prove that all unitary graphs are connected of diameter two and girth three. Based on this, we obtain, for any prime power , a lower bound of order on the maximum number of vertices in an arc-transitive graph of degree and diameter two.