图的邻点可区别全染色(AVDTC)数为χat(G),有猜想:χat(G)≤△(G)+3.联图Ws ∨ Km,n的邻点可区别全色数被确定为χat(Ws ∨ Km,n)=△(Ws ∨ Km,n)+1或△(Ws ∨ Km,n)+2.
A conjecture about the concept of the adjacent-vertex distinguishing total colorings (AVDTC) on graphs is stated as this: For any simple graph G, then Xat (G) ≤△(G) + 3. The AVDTC-chromatic number of a join graph Ws∨ Km,n is determined in the form △( Ws∨ Km,n) +1≤χat ( Ws ∨ Km,n) ≤△( Ws ∨ Km,n) +2.