摘要
Let G^o be complementary graph of a graph G. x_T(G) denotes the total charomatic number of G. We obtain Theorem. Let G be a simple graph and |V(G)|=2n, n>1. Then (1) 2n+1≤X_T(G)+X_T(G^o)≤4n-1; (2) 2n≤X_T(G)·X_T(G^o)≤2n(2n-1). We have two examples. (1) When G={1}+{2}, then X_T(G)+X_T(G^o)=4; (2) For every n>1, we take G=K(2n-1)+{2n}, then X_T(G)+X_T(G^o)=4n-1.
