مشخصات پژوهش

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).