graph labeling
assignment of labels, traditionally represented by integers, to the edges or vertices, or both, of a graph
graceful labeling
assignment of integer labels to the vertices of a graph that uniquely identifies edges by the difference of their endpoint labels
graph coloring
assignment of colors to elements of a graph subject to certain constraints
total coloring
proper graph coloring of both vertices and edges
distinguishing coloring
graph labeling that destroys all symmetries