Abstract

The energy of a graph G, denoted by E(G), is defined as the sum of absolute values of all eigenvalues of G. In (MATCH Commun. Math. Comput. Chem. 83 (2020) 631–633) it was conjectured that for every graph G with maximum degree
∆(G) and minimum degree δ(G) whose adjacency matrix is nonsingular, E(G) ≥ ∆(G) + δ(G) and the equality holds if and only if G is a complete graph. Here, we prove the validity of this conjecture for planar graphs, trianglefree graphs and
quadranglefree graphs.
