Abstract

The energy E(G) of a graph G is the sum of the absolute values of all eigenvalues
of G. Zhou in (MATCH Commun. Math. Comput. Chem. 55 (2006) 91{94) studied
the problem of bounding the graph energy in terms of the minimum degree together
with other parameters. He proved his result for quadranglefree graphs. Recently,
in (MATCH Commun. Math. Comput. Chem. 81 (2019) 393{404) it is shown that
for every graph G, E(G) ≥ 2δ(G), where δ(G) is the minimum degree of G, and the
equality holds if and only if G is a complete multipartite graph with equal size of
parts. Here, we provide a short proof for this result. Also, we give an affirmative
answer to a problem proposed in (MATCH Commun. Math. Comput. Chem. 81
(2019) 393{404).
