(adj.), isomorphism (n.): These are central notions not just in graph theory but in all of modern mathematics. Two mathematical objects, call them A and B, are isomorphic if they have the same structure; that is, if there is a 1:1 map from A to B that preserves all of the structure relevant to these objects. Such a map is an isomorphism. When A,B are graphs, an isomorphism is a bijection from the vertices of A to the vertices of B such that any two vertices of A are adjacent if and only if their images in B are adjacent. For example, the pentagon and pentagram are isomorphic as graphs; one isomorphism takes vertices 1,2,3,4,5 to 1,3,5,2,4. If A and B are isomorphic then they have identical graph-theoretical properties; for instance, since the pentagon is regular of degree 2, with diameter 2 and girth 5, the same is automatically true also of the pentagram once we know that the two graphs are isomorphic.