Abstract: Consider the space of cycle graphs with $n$ vertices embedded in $\mathbb{R}^3$, such that lengths of edges are $\leq 1$. Define the energy function with power $p$ to be the sum of $p$-th powers of all distances between different vertices. We discuss the symmetry break behavior of energy maximizing graphs as $n$ and $p$ range, theoretically and numerically. Joint work with Zhongzi Wang.
