Proper

Summary

A proper subgraph is a subgraph that removes at least one vertex or edge relative to the whole graph; for finite graphs, proper subgraphs are never isomorphic to the whole graph, but for infinite graphs they can be.

A proper coloring is an assignment of colors to the vertices of a graph (a coloring) that assigns different colors to the endpoints of each edge; see color.

A proper interval graph or proper circular arc graph is an intersection graph of a collection of intervals or circular arcs (respectively) such that no interval or arc contains another interval or arc. Proper interval graphs are also called unit interval graphs (because they can always be represented by unit intervals) or indifference graphs.