ABSTRACT
In a vertex labeling of a graph G, each vertex of G is assigned a label (an element of some set). If distinct vertices are assigned distinct labels, then the labeling is called vertex-distinguishing or irregular. That is, each vertex of G is uniquely determined by its label. A vertex labeling of G in which every two adjacent vertices are assigned distinct labels is a neighbor-distinguishing labeling. Similarly, an edge labeling of G is edge-distinguishing if distinct edges are assigned distinct labels. There are occasions when a vertex coloring of a graph gives rise to an edgedistinguishing labeling and occasions when an edge coloring may induce a vertexdistinguishing labeling or a neighbor-distinguishing labeling. Vertex colorings may also induce vertex-distinguishing labelings. Colorings that induce distinguishing labelings of some type are themselves called distinguishing colorings, which is the subject of this chapter.
