A new approach for the characteristic polynomial of a complete tripartite graph

The case k = 3 of a complete k-partite graph is called tripartite Tp,q,r. It that its vertices are decomposed into three disjoint sets such that, no two within the same set adjacent. has recently attracted much attention due to important in several applications, especially, chemistry where some molecular orbital compounds correspondents structure. One method capturing structure through computing characteristic polynomial for matrix characterization M graph, which defined as determinant | λI – I identity and λ variable polynomial. general technique polynomials evaluation graphs with large number considered an extremely tiresome problem when it based on matrix, because computational complexity high. In this paper, new approach Ti,i,n−2i, n ≥ 4, adjacency introduced. shows good efficiency reduces difficulty computation comparing well-known methods vertices.