<P> The degree of a vertex, denoted δ (v) in a graph is the number of edges incident to it . An isolated vertex is a vertex with degree zero; that is, a vertex that is not an endpoint of any edge (the example image illustrates one isolated vertex). A leaf vertex (also pendant vertex) is a vertex with degree one . In a directed graph, one can distinguish the outdegree (number of outgoing edges), denoted δ (v), from the indegree (number of incoming edges), denoted δ (v); a source vertex is a vertex with indegree zero, while a sink vertex is a vertex with outdegree zero . A simplicial vertex is one whose neighbors form a clique: every two neighbors are adjacent . A universal vertex is a vertex that is adjacent to every other vertex in the graph . </P> <P> A cut vertex is a vertex the removal of which would disconnect the remaining graph; a vertex separator is a collection of vertices the removal of which would disconnect the remaining graph into small pieces . A k - vertex - connected graph is a graph in which removing fewer than k vertices always leaves the remaining graph connected . An independent set is a set of vertices no two of which are adjacent, and a vertex cover is a set of vertices that includes at least one endpoint of each edge in the graph . The vertex space of a graph is a vector space having a set of basis vectors corresponding with the graph's vertices . </P> <P> A graph is vertex - transitive if it has symmetries that map any vertex to any other vertex . In the context of graph enumeration and graph isomorphism it is important to distinguish between labeled vertices and unlabeled vertices . A labeled vertex is a vertex that is associated with extra information that enables it to be distinguished from other labeled vertices; two graphs can be considered isomorphic only if the correspondence between their vertices pairs up vertices with equal labels . An unlabeled vertex is one that can be substituted for any other vertex based only on its adjacencies in the graph and not based on any additional information . </P> <P> Vertices in graphs are analogous to, but not the same as, vertices of polyhedra: the skeleton of a polyhedron forms a graph, the vertices of which are the vertices of the polyhedron, but polyhedron vertices have additional structure (their geometric location) that is not assumed to be present in graph theory . The vertex figure of a vertex in a polyhedron is analogous to the neighborhood of a vertex in a graph . </P>

A vertex may also be called a node