Abstract
For a simple graph \(G\), the Seidel energy, denoted by \(\mathcal{E}(\mathcal{S}(G))\), is defined as the sum of absolute values of all eigenvalues of the Seidel matrix of \(G\). Two graphs are called \(SC\)-equivalent if one of them is obtained from
the other or its complement by a Seidel switching. In [3] Haemers conjectured that if \(G\) is a graph of order \(n\), then \(\mathcal{E}(\mathcal{S}(G)) \geq 2n - 2\). Recently, in [S. Akbari, M. Einollahzadeh, M.M. Karkhaneei, M. A.
Nematollahi, Proof of a conjecture on the Seidel energy of graphs, European J. Combin. 86 (2020): 103078] the authors proved this conjecture and showed that if \(G\) is a graph of order \(n\), then \(\mathcal{E}(\mathcal{S}(G)) \geq 2n
- 2\) and the inequality is strict provided that \(G\) is not \(SC\)-equivalent to \(K_{n}\). In this paper, we improve this lower bound and show that if \(G\) is a graph of order \(n \geq 7\) which is not \(SC\)-equivalent to \(K_{n}\),
then \(\mathcal{E}(\mathcal{S}(G)) > 2n - 1\).