On the energy of line graphs.

The energy of a graph G , E (G) , is defined as the sum of absolute values of the eigenvalues of its adjacency matrix. In Akbari and Hosseinzadeh (2020) [3] it was conjectured that for every graph G with maximum degree Δ (G) and minimum degree δ (G) whose adjacency matrix is non-singular, E (G) ≥ Δ (G) + δ (G) and the equality holds if and only if G is a complete graph. Let G be a connected graph with the edge set E (G). In this paper, first we show that E (L (G)) ≥ | E (G) | + Δ (G) − 5 , where L (G) denotes the line graph of G. Next, using this result, we prove the validity of the conjecture for the line of each connected graph of order at least 7. [ABSTRACT FROM AUTHOR]