Abstract:

The adjacentvertexdistinguishing total chromatic number of K^c_r∨K_s, the join of empty graph of order r and complete graph of order s, was discussed via the method of combinatory analysis. One important result χ_at(K^c_r∨K_s)=r+s+2 holds when r+s is an odd number and s>r²+2r-1, where χ_at(G)  represents the adjacent\|vertex\|distinguishing total chromatic number.

Key words: adjacentvertexdistinguishing total coloring, adjacentvertexdistinguishing total chromatic number, join of graphs