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What Graphs are 2-Dot Product Graphs?
Johnson, Matthew...

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What Graphs are 2-Dot Product Graphs? by Johnson, Matthew ( Author )
Lemonjar Open Access
N.A
02-08-2023
Let $d \geq 1$ be an integer. From a set of $d$-dimensional vectors, we obtain a $d$-\dpg\ by letting each vector $\va^u$ correspond to a vertex $u$ and by adding an edge between two vertices $u$ and $v$ if and only if their dot product $\va^{u} \cdot \va^{v} \geq t$, 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 $d\geq 2$. 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.
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Article
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37.08 KB
English
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MYR 0.01
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http://arxiv.org/abs/1511.05009
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