Borderenergetic graphs of order 12

Abstract

A graph \(G\) of order \(n\) is said to be borderenergetic if its energy is equal to \(2n-2\) and if \(G\) differs from the complete graph \(K_n\). The first such graph was discovered in 2001, but their systematic study started only in 2015. Until now, the number of borderenergetic graphs of order \(n\) was determined for \(n \leq 11\). We now establish that there exist exactly 572 connected borderenergetic graphs of order 12.