Jill Bigley Dunham

*
Extremal coin graphs on multiple radii
*

**Abstract:**
In this talk, we will consider extremal coin graphs in the Euclidean plane. A
coin graph is a graph whose vertices can be represented as the centers of
closed, non-overlapping disks in the Euclidean plane such that two vertices are
adjacent if and only if their corresponding disks are tangent.
The problem of determining the maximum number of edges of a unit coin graph on
n vertices has been solved previously by Heiko Harborth. We will generalize the
problem to coin graphs with multiple possible radii in a couple of different
ways. A motivating problem is a special case of a coin graph with two possible
radii. Another motivating problem is a classical problem of tangent circles
known as Soddy circles.