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What graphs are 2-dot product graphs?

Johnson, M. and Paulusma, D. and van Leeuwen, E.J. (2021) 'What graphs are 2-dot product graphs?', International Journal of Computational Geometry and Applications, 31 (01). pp. 1-16.

Abstract

Let d ≥ 1 be an integer. From a set of d-dimensional vectors, we obtain a d-dot product graph by letting each vector a u correspond to a vertex u and by adding an edge between two vertices u and v if and only if their dot product a u · a v ≥ 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.

Item Type:Article
Full text:Publisher-imposed embargo until 10 September 2022.
(AM) Accepted Manuscript
File format - PDF
(381Kb)
Status:Peer-reviewed
Publisher Web site:https://doi.org/10.1142/S0218195921500011
Publisher statement:Electronic version of an article published as International Journal of Computational Geometry & Applications, 31, 01, 2021, 1-16, 10.1142/S0218195921500011. © [copyright World Scientific Publishing Company] https://www.worldscientific.com/doi/10.1142/S0218195921500011
Date accepted:26 June 2021
Date deposited:24 August 2021
Date of first online publication:10 September 2021
Date first made open access:10 September 2022

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