An improved lower bound for the Seidel energy of tree graphs

Abstract

Let $G$ be a graph with the vertex set $ \lbrace v_1,\ldots,v_n \rbrace$. The Seidel matrix of $G$ is an $n\times n$ matrix whose diagonal entries are zero, $ij$-th entry is $-1$ if $ v_{i} $ and $ v_{j} $ are adjacent and otherwise is $ 1 $. The Seidel energy of $G$, denoted by $ \se{G} $, is defined to be the sum of absolute values of all eigenvalues of the Seidel matrix of $G$. In \cite{aekn}, the authors proved that the Seidel energy of any graph of order $n$ is at least $2n-2$. In this study, we improve the aforementioned lower bound for tree graphs.