Datensatz

Zusammenfassung

Let $d \geq 1$ be an integer. From a set of $d$-dimensional vectors, we obtain a $d$-dot product graph by letting each vector ${\bf a}^u$ correspond to a vertex $u$ and by adding an edge between two vertices $u$ and $v$ if and only if their dot product ${\bf a}^{u} \cdot {\bf a}^{v} \geq t$, 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.