New tools for the construction of directed strongly regular graphs: Difference digraphs and partial sum families

  • Authors:

  • Luis Martínez;Alexander Araluze

  • Affiliations:

  • Departamento de Matemáticas, Universidad del País Vasco, 48080 Bilbao, Spain;Departamento de Matemáticas, Universidad del País Vasco, 48080 Bilbao, Spain

  • Venue:
  • Journal of Combinatorial Theory Series B
  • Year:
  • 2010

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Abstract

We define a class of digraphs involving differences in a group that generalizes Cayley digraphs, that we call difference digraphs. We define also a new combinatorial structure, called partial sum family, or PSF for short, from which we obtain difference digraphs that are directed strongly regular graphs. We give an infinite family of PSFs and we give also twelve sporadic ones that generate directed strongly regular graphs whose existence was previously undecided.