The change of Seidel energy of 5-partite Turán graph due to edge deletion

Abstract

Let G be a simple undirected graph. The Seidel energy of G, denoted by Es(G), is the sum of absolute values of all Seidel eigenvalues of G. A complete r-partite graph with n vertices is called r-partite Turán graph, denoted by T(n,r), if the number of vertices of each part is either ⌊nr⌋ or ⌈nr⌉. In 2021, Tian et al. proposed a problem that for any edge e of Turán graph T(n,r) with r≥4, does there exist a sufficiently large integer n0 such that Es(T(n,r))<Es(T(n,r)−e) whenever n≥n0. In this paper, we prove that the Seidel energy of T(n,5) of order n≥5 is always increased when an edge is deleted.