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R. Graham, M. Simonovits, and V.T. Sós [R. Graham, M. Simonovits, V.T. Sós, A note on the intersection properties of subsets of integers, J. Combin. Theory, Ser. A 28 (1980) 106–110] in 1980 posed the following question. Suppose S is a convex subset of Zk and let A be a family of subsets of S such that Ai∩Aj is convex and nonempty for Ai,Aj∈A,Ai≠Aj. If A is a family of maximum cardinality with this...
A graph is one-regular if its automorphism group acts regularly on the set of its arcs. In this paper, we construct infinitely many one-regular graphs of valency 4 and 6. These graphs are Cayley graphs on dihedral groups.
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