MATH 100 MIDTERM EXAM STUDY GUIDE
Graph - Answers -set of vertices and set of edges, represented as a set of pairs of
vertices
Complete Graph - Answers -A graph in which every pair of vertices is joined by an
edge exactly once.
Simple Graph - Answers -Has no loops and is not a multigraph.
Order - Answers -The order of G is the number of vertices in G.
Size - Answers -The size of G is the number of edges in G.
Adjacent - Answers -Two vertices (u and v) are adjacent if the graph contains an edge
uv, joining the vertices u and v
Degree of a Vertex - Answers -in the graph is the number of edges of G incident with v
except that a loop contributes twice to the degree of the vertex.
Graphic - Answers -A sequence of numbers is graphic if it is the degree sequence of a
simple graph.
Tournament - Answers -directed graph where for each pair of vertices u and v either uv
or vu an edge of T. one way to create a tournament is to start with a complete graph
and assign a direction to each edge.
Out degree - Answers -The number of edges directed from v and is denoted by od v.
the outrigger of a vertex is also the score of the vertex.
Transmitter - Answers -a vertex v with id v=0 and od v some number bigger than 0
Reciever - Answers -a vertex with od v= 0 and id v some number bigger than 0.
Digraph (Directed Graph) - Answers -Graph in which each edge has a direction
associated with it.
Isomorphic - Answers -if the vertices of the two graphs can be labeled with the
numbers from 1 to n.
Isomorphic: - Answers -Must have same:
-number of vertices
-number of edges
-degree sequence of the vertices
Graph - Answers -set of vertices and set of edges, represented as a set of pairs of
vertices
Complete Graph - Answers -A graph in which every pair of vertices is joined by an
edge exactly once.
Simple Graph - Answers -Has no loops and is not a multigraph.
Order - Answers -The order of G is the number of vertices in G.
Size - Answers -The size of G is the number of edges in G.
Adjacent - Answers -Two vertices (u and v) are adjacent if the graph contains an edge
uv, joining the vertices u and v
Degree of a Vertex - Answers -in the graph is the number of edges of G incident with v
except that a loop contributes twice to the degree of the vertex.
Graphic - Answers -A sequence of numbers is graphic if it is the degree sequence of a
simple graph.
Tournament - Answers -directed graph where for each pair of vertices u and v either uv
or vu an edge of T. one way to create a tournament is to start with a complete graph
and assign a direction to each edge.
Out degree - Answers -The number of edges directed from v and is denoted by od v.
the outrigger of a vertex is also the score of the vertex.
Transmitter - Answers -a vertex v with id v=0 and od v some number bigger than 0
Reciever - Answers -a vertex with od v= 0 and id v some number bigger than 0.
Digraph (Directed Graph) - Answers -Graph in which each edge has a direction
associated with it.
Isomorphic - Answers -if the vertices of the two graphs can be labeled with the
numbers from 1 to n.
Isomorphic: - Answers -Must have same:
-number of vertices
-number of edges
-degree sequence of the vertices
