Abstract. An eccentric sequence of a connected finite graph is a sequence of eccentricities of its vertices. An eccentric sequence is called minimal if it has no proper eccentric subsequence with the same number of distinct eccentricities. We survey known results concerning minimal two-valued eccentric sequences and describe a new infinite class of these sequences. Also a conjecture on all minimal two-valued eccentric sequences is proposed.

Received: December 14, 2011

AMS Subject Classification: 05C12

Key Words and Phrases: cycle, eccentricity, eccentric sequence, minimal eccentric sequence

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