isolated -

no neighbors

neighbor -

u and v are neighbors if there is an edge {u,v} in the graph

vertex -

node, point ....

arc -

arrow, directed line, directed edge, directed link.....

graph -

a pair (V, E) where V is a set and E is a set of ordered pairs of elements in V. V will be called the set of vertices and E will be called the set of edges.

planar graph-

a graph formed by a polyhedron that is embedded such that all of the edges form straight lines.

directed graph or digraph -

a pair (V,A) where V is a set and A is a set of ordered pairs of elements in V. V will be called the set of vertices and A will be called the set of arcs. In a directed graph, no multiple arcs are allowed.

Multigraph or Multidigraph -

multiple edges/arcs are allowed within this directed graph.

Jordan curve -

a simple closed curve that divides the plane into two regions. A homeomorphic mapping from a circle is one to one.

chain -

a sequence in a graph G {u1,e1,u2,e2,....ut,et,ut+1}

where the set of vertices {u1, ...,ut+1} is a non-empty set and the set of edges {e1, ... , et+1} is a non- empty set.

closed chain -

if u1 = ut+1 where u1 is the beginning of the chain and ut+1 is the end of the chain.

circuit -

simple closed chain

Eulerian Chain -

in a Multigraph an Eulerian chain uses every edge once and only once.

Eulerian Closed Chain -