Graph designs for the eight-edge five-vertex graphs

Charles Colbourn, Gennian Ge, Alan C H Ling

Research output: Contribution to journalArticlepeer-review

5 Scopus citations

Abstract

The existence of graph designs for the two nonisomorphic graphs on five vertices and eight edges is determined in the case of index one, with three possible exceptions in total. It is established that for the unique graph with vertex sequence (3, 3, 3, 3, 4), a graph design of order n exists exactly when n ≡ 0, 1 (mod 16) and n ≠ 16, with the possible exception of n = 48. For the unique graph with vertex sequence (2, 3, 3, 4, 4), a graph design of order n exists exactly when n ≡ 0, 1 (mod 16), with the possible exceptions of n ∈ {32, 48}.

Original languageEnglish (US)
Pages (from-to)6440-6445
Number of pages6
JournalDiscrete Mathematics
Volume309
Issue number22
DOIs
StatePublished - Nov 28 2009

Keywords

  • Decomposition
  • G-designs
  • G-designs
  • Graph designs

ASJC Scopus subject areas

  • Theoretical Computer Science
  • Discrete Mathematics and Combinatorics

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