The basics
a point on a network graph
what is a vertex?
the name given when more than one edge connects two vertices
What are multiple edges?
The name given to a graph where each vertex can be reached by any other vertex
What is a connected graph?
the matrix form of a network graph
What is an adjacency matrix?
a sequence of edges, linking successive vertices, that connects two different vertices in a graph.
what is a walk?
line joining two vertices
what is an edge?
a vertex not connected to any others
What is an isolated vertex?
a a smaller selection of a larger network graph
What is a sub graph?
the name given to graphs that are identical in the number of vertices and number of edges and the same connections between vertices
What are isomorphic graphs?
a walk with edges that are not repeated and vertices that can be repeated
what is a trail?
what is the degree?
the relationship that relates the number of edges to the sum of the degrees of the vertices
What is d=2e (or e=d/2)
the name given when every vertex has the same degree
What is a regular degree?
The name given when a graph is re-drawn so that no edges intersect each other
What is a planar graph?
a walk with edges that are not repeated and vertices that are not repeated
what is a path?
vertices directly connected to each other
What are adjacent vertices?
a network graph with no multiple edges or loops
What is a simple graph?
a simple graph that has every vertex connected to every other vertex
What is a complete graph?
v+f-e=2
what is euler's formula?
a walk that starts and ends at the same vertex and edges that are not repeated but vertices that can be repeated
what is a circuit?
The name given when a vertex is connected to itself
What is a loop?
A network graph with no edges
What is a degenerate graph?
the mathematical expression you can use to find the number of edges and degree of vertices in a complete graph with n vertices
What is (n-1) for the degree of each vertex and what is n(n-1)/2 for the number of edges?
the name given to an edge that when removed from a connected graph leaves the graph disconnected
what is a bridge?
a walk that starts and ends at the same vertex and edges that are not repeated and vertices that are not repeated
what is a cycle?