About cookies on this site Our websites require some cookies to function properly (required). In addition, other cookies may be used with your consent to analyze site usage, improve the user experience and for advertising. For more information, please review your options. By visiting our website, you agree to our processing of information as described in IBM’sprivacy statement. To provide a smooth navigation, your cookie preferences will be shared across the IBM web domains listed here.
Publication
Discrete Mathematics
Paper
Counterexamples to two conjectures about distance sequences
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 sequences 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. © 1987.