Graph on the cover of Bollobás's "Combinatorics" I was browsing the library and I found Bela Bollobás book "Combinatorics: Set Systems, Hypergraphs, Families of Vectors and Probabilistic Combinatorics" and, on its cover, it has a graph that I don't quite recognize: !Graph from the cover Is this graph any "interesting", as used for counterexamples (e.g., Petersen's Graph)? I could determine some of its characteristics (9 vertices, regular of valency 4, non-planar, diameter 2 etc.), but is it distinguished in any way for being featured in an important book?

This graph is known as the generalized quadrangle (2,1), it is also the line graph of the $K_{3,3}$, as well as the Paley-9 graph. See here for more information. I am not aware that it is used as a prominent counterexample.