What Graphs are 2-Dot Product Graphs?

Matthew Johnson, Daniël Paulusma, Erik Jan van Leeuwen

Research output: Contribution to journalArticleAcademicpeer-review


Let d≥1 be an integer. From a set of d-dimensional vectors, we obtain a d-dot product graph by letting each vector au correspond to a vertex u and by adding an edge between two vertices u and v if and only if their dot product au⋅av≥t, for some fixed, positive threshold t. Dot product graphs can be used to model social networks. Recognizing a d-dot product graph is known to be NP-hard for all fixed d≥2. To understand the position of d-dot product graphs in the landscape of graph classes, we consider the case d=2, and investigate how 2-dot product graphs relate to a number of other known graph classes including a number of well-known classes of intersection graphs.
Original languageEnglish
Pages (from-to)1-16
JournalInternational Journal of Computational Geometry and Applications
Issue number1
Publication statusPublished - 2021


  • Dot product graph
  • 2-dot product graphs
  • dot product dimension
  • co-bipartitegraphs
  • intersection graphs
  • unit disk graphs
  • circular-arc graphs
  • split graphs
  • socialnetworks


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