Abstract: We construct a family of vertex transitive graphs on a left loop structure of order 2q^2 where q is a power of a prime such that q\equiv 1 \bmod 4. The graphs are of diameter 2. The smallest of these graphs is isomorphic to the Hoffman-Singleton graph.
Keywords: left loop; quasi-associative; Cayley graph; Hoffman-Singleton graph; vertex transitive
DOI: DOI 10.14712/1213-7243.2025.009
AMS Subject Classification: 05C25 05C60 05C62 05E18