Abstract
A graph \(G\) of order \(n\) is borderenergetic if it has the same energy as the complete graph \(K_n\). In this paper, we obtain the result that for any connected graph \(G\), except for the five graphs (one of order 5, three of order 6 and one of order 10), the line graph \(L(G)\) of \(G\) is not borderenergetic. As a consequence, we get that if \(G\) is a borderenergetic graph, then the line graph \(L(G)\) of \(G\) is not borderenergetic. In addition, we observe a relation between the lower bound of the energy of the line graph \(L(G)\) of a borderenergetic graph \(G\) and the minimum degree \(\delta(G)\) of \(G\).
