The Seidel energy of a simple and undirected graph \(\Gamma\) , denoted by \(SE(\Gamma )\) , is the sum of the absolute values of the eigenvalues of the Seidel matrix \(S(\Gamma )\) of \(\Gamma\) . The Seidel energy is a valuable tool for analyzing the structural properties of networks. This paper investigates how this energy changes when the topology of a graph is locally perturbed by embedding a new edge. We focus on the tripartite Turán graph T(n, 3), a model of extremal network connectivity. When an edge \(e=u_1u_2\) is embedded in the tripartite Turán graph \(T(8,3)\cong K_{\{u_1,u_2\},\{v_1,v_2,v_3\},\{w_1,w_2,w_3\}}\) , then \(SE(T(8,3)+e)\approx 16.9282 < SE(T(8,3))\approx 17.2111\) . It is proved that except for T(8, 3), the Seidel energy of the tripartite Turán graph T(n, 3) with order at least 8 is always increased when an edge is embedded. This result has implications for dynamically understanding the sensitivity and stability of network descriptors.
