Group for Research in Decision Analysis

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

## Seyed Ahmad Mojallal and Pierre Hansen

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