This web page contains the abstract of my paper:
"Counterexamples to Two Conjectures about Distance Sequences" with M.E. Watkins, Discrete Mathematics, 66(1987), p. 289-298.
Abstract: It is shown that contrary to a pair of well known conjectures, there exist finite and infinite examples of: (1) vertex-transitive graphs whose distance sequences are not unimodal, and (2) graphs with primitive automorphism group whose distance sequnces are not logarithmically convex. In particular, a family of finite graphs is presented whose automorphism groups are primitive and whose distance sequences are not unimodal.
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