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Abstract
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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 quadrangle-free 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).
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