On Borderenergetic graphs

Ivan Gutman

A graph $G$ of order $n$ is said to be borderenergetic if its energy is equal to $2n-2$ and if $G \not \cong K_n$. The first such graph was discovered in 2001, but their systematic study started only in 2015. The main hitherto established results on borderenergetic graphs are outlined, and a few new established. Borderenergetic graphs (of the same order) are mutually equienergetic. The difference in their structure indicates which structural features of a graph can vary, without affecting the value of its energy. In particular, it is shown that this applies to the number of edges.