Links between two semisymmetric graphs on 112 vertices via association schemes

Mikhail Klin, Josef Lauri, Matan Ziv-Av

Research output: Contribution to journalArticlepeer-review

5 Scopus citations


This paper provides a model of the use of computer algebra experimentation in algebraic graph theory. Starting from the semisymmetric cubic graph . L on 112 vertices, we embed it into another semisymmetric graph . N of valency 15 on the same vertex set. In order to consider systematically the links between . L and . N, a number of combinatorial structures are involved and related coherent configurations are investigated. In particular, the construction of the incidence double cover of directed graphs is exploited. As a natural by-product of the approach presented here, a number of new interesting (mostly non-Schurian) association schemes on 56, 112 and 120 vertices are introduced and briefly discussed. We use computer algebra system GAP (including GRAPE and nauty), as well as computer package COCO.

Original languageEnglish
Pages (from-to)1175-1191
Number of pages17
JournalJournal of Symbolic Computation
Issue number10
StatePublished - 1 Oct 2012


  • Association scheme
  • Computer algebra
  • Dejter graph
  • Deza graph
  • Double cover
  • Ljubljana graph
  • Nikolaev graph
  • Overlarge set of designs
  • Semisymmetric graph

ASJC Scopus subject areas

  • Algebra and Number Theory
  • Computational Mathematics


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