Prefer a chat interface with context about you and your work?
The minimum size and maximum diameter of an edge-pancyclic graph of a given order
A $k$-cycle in a graph is a cycle of length $k.$ A graph $G$ of order $n$ is called edge-pancyclic if for every integer $k$ with $3\le k\le n,$ every edge of $G$ lies in a $k$-cycle. It seems difficult to determine the minimum size $f(n)$ of a simple edge-pancyclic …