Abstract:Let G be a simple graph and di be the degree of the vertex vi. The Seidel Laplacian matrix of a graph G is a real symmetric matrix with diagonal elements of n-1-2di and off-diagonal elements of ±1. If the vertices vi and vj are adjacent, (SL(G))ij=1, and otherwise, (SL(G))ij=-1. The Seidel Laplacian-Estrada index was introduced and investigated. The upper and lower bounds for the Seidel Laplacian-Estrada index, and the relationship between the Seidel Laplacian-Estrada index and the Seidel Laplacian energy are provided.