Let GGG be a graph. A total coloring is a function g:V∪E→{1,2,…,k}g:V\cup E\to\{1,2,\dots,k\}g:V∪E→{1,2,…,k}, with total vertex weight σt(v)=g(v)+∑v∈eg(e)\sigma^t(v)=g(v)+\sum_{v\in e}g(e)σt(v)=g(v)+∑v∈eg(e). Adjacent vertices are distinguished…
Let GGG be a graph without isolated edges. An edge coloring f:E→{1,2,…,k}f:E\to\{1,2,\dots,k\}f:E→{1,2,…,k} assigns a weight σ(v)=∑v∈ef(e)\sigma(v)=\sum_{v\in e}f(e)σ(v)=∑v∈ef(e) to each vertex; adjacent vertices are distinguish…
