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Durham University

Computer Science

Profile

Publication details for Professor Matthew Johnson

Johnson, M., van Leeuwen, E.J. & Paulusma, D. (2015), What graphs are 2-dot product graphs?, Electronic Notes in Discrete Mathematics 49: The Eight European Conference on Combinatorics, Graph Theory and Applications, EuroComb 2015. Bergen, Norway, Elsevier, Bergen, 705-711.

Author(s) from Durham

Abstract

From a set of d-dimensional vectors for some integer d ≥ 1, 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. 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.