Neighbor Vertex and Neighborhood
We write vivj Î E(G) to mean {vi, vj}Î E(G), and if e = vi vj Î E(G), we say vi and vj are adjacent.
Formally, given a graph G = (V, E), two vertices vi , vj Î V are said to be neighbors, or adjacent nodes, if ( vi , vj ) Î E. If G is directed, we distinguish between incoming neighbors of vi (those vertices vj Î V such that (vj, vi) Î E) and outgoing neighbors of vi (those vertices vj ÎV such that (vi, vj) Î E).
The open neighborhood N(v) of the vertex v consists of the set vertices adjacent to v, that is, N(v) = {w Î v : vw Î E}. The closed neighborhood of v is N[v] = N(v) È {v}. For a set S Í V, the open neighborhood N(S) is defined to be UvÎSN(v), and the closed neighborhood of S is N[S] = N(S) È S.
We write vivj Î E(G) to mean {vi, vj}Î E(G), and if e = vi vj Î E(G), we say vi and vj are adjacent.
Formally, given a graph G = (V, E), two vertices vi , vj Î V are said to be neighbors, or adjacent nodes, if ( vi , vj ) Î E. If G is directed, we distinguish between incoming neighbors of vi (those vertices vj Î V such that (vj, vi) Î E) and outgoing neighbors of vi (those vertices vj ÎV such that (vi, vj) Î E).
The open neighborhood N(v) of the vertex v consists of the set vertices adjacent to v, that is, N(v) = {w Î v : vw Î E}. The closed neighborhood of v is N[v] = N(v) È {v}. For a set S Í V, the open neighborhood N(S) is defined to be UvÎSN(v), and the closed neighborhood of S is N[S] = N(S) È S.