An extension on neighbor sum distinguishing total coloring of graphs

Jing-zhi Chang, Chao Yang, Zhi-xiang Yin +1

Let $f:V(G)\cup E(G)\to \{1,2,\dots ,k\}$ be a non-proper total $k$-coloring of $G$. Define a weight function on total coloring as $$ϕ(x)=f(x)+\sum\limits_{e\ni x}f(e)+\sum…