Groupe d’études et de recherche en analyse des décisions

G-2020-05

On the difference of energies of a graph and its complement graph

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The energy of a graph \(G\), denoted by \({\cal E}(G)\), is defined as the sum of the absolute values of all eigenvalues of \(G\). In this paper we study the difference of energies of a (regular) graph \(G\) and its complete graph \(\overline{G}\), that is, \({\cal E}(G)-{\cal E}(\overline{G})\). In particular, we provide the answer to Problem 12 raised in Nikiforov (2016). Moreover, we give a lower bound for the energy of a regular graph in terms of the order and the clique cover number.

, 12 pages