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Graphs with unique walks, trails or paths of given lengths

Part of the Lecture Notes in Mathematics book series (LNM,volume 642)

Abstract

In this paper we consider directed, undirected, or mixed graphs G. We also assume that for any two vertices u and v of G there exists exactly one walk [trail, path] from u to v whose length is in a given interval. Mixed Moore graphs (as special kinds of such graphs) are also studied. It is shown that there exist infinitely many mixed Moore graphs of diameter two. Some of the proofs are indicated and some will be published elsewhere.

Keywords

  • Directed Graph
  • Undirected Graph
  • Regular Graph
  • Cardinal Number
  • Petersen Graph

These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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References

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© 1978 Springer-Verlag Berlin Heidelberg

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Bosák, J. (1978). Graphs with unique walks, trails or paths of given lengths. In: Alavi, Y., Lick, D.R. (eds) Theory and Applications of Graphs. Lecture Notes in Mathematics, vol 642. Springer, Berlin, Heidelberg. https://doi.org/10.1007/BFb0070366

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  • DOI: https://doi.org/10.1007/BFb0070366

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  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-08666-6

  • Online ISBN: 978-3-540-35912-8

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