Iofinova and Ivanov (1985) showed that there exist exactly five bipartitecubic semisymmetric graphs whose automorphism
groups preserves the bipartite parts and acts primitively on each part. These graphs
have 110, 126, 182, 506, and 990 vertices, and their automorphism groups are , , , , and , respectively, where is one of the Mathieu groups.
The smallest Iofinova-Ivanov graph is the graph on 110 vertices illustrated above in two embeddings which is the second smallest cubic
semisymmetric graph (Iofinova and Ivanov 2002, Marušič et al.
2005). It was constructed in Ivanov (1983) in terms of the Paley design .
The 110-vertex Iofinova-Ivanov graph is illustrated above in three LCF
notations of degree 11 and four of degree 5.
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