Let G be a simple graph and A(G) be the adjacency matrix of G. The matrix \(S(G) = J -I -2A(G)\) is called the Seidel matrix of G, where I is an identity matrix and J is a square matrix all of whose entries are equal to 1. Clearly, if G is a graph of order n with no isolated vertex, then the Seidel matrix of G is also the adjacency matrix of a signed complete graph \(K_n\) whose negative edges induce G. In this paper, we study the Seidel eigenvalues of the complete multipartite graph \(K_{n_1,\ldots ,n_k}\) and investigate its Seidel characteristic polynomial. We show that if there are at least three parts of size \(n_i\), for some \(i=1,\ldots ,k\), then \(K_{n_1,\ldots ,n_k}\) is determined, up to switching, by its Seidel spectrum.

让G ^是一个简单图和甲（ģ）是邻接矩阵G ^。矩阵\（S（G）= J -I -2A（G）\）称为G的Seidel矩阵，其中I是一个单位矩阵，J是一个平方矩阵，所有条目都等于1。如果G是n阶的图，没有孤立的顶点，则G的Seidel矩阵也是带负数的G的有符号完整图\（K_n \）的邻接矩阵。在本文中，我们研究了完整的多部分图的Seidel特征值\（K_ {n_1，\ ldots，n_k} \）并研究其Seidel特征多项式。我们表明，如果至少有三个大小\（n_i \），对于某些\（i = 1，\ ldots，k \），则确定\（K_ {n_1，\ ldots，n_k} \），直至通过其Seidel光谱进行切换。