Quantitive Reasoning Ch. 13 Terms

Euler's Formula

V-E+F=2

tree

A connected graph with no cycles

Regular Graph

A graph in which every vertex has the same degree.

Bipartite graph

A graph in which the vertices are partitioned into two disjoint groups, e.g. males and females

disconnected graph

A graph that has at least one pair of vertices not joined by a path

Spanning tree

A subgraph of a connected graph that is a tree and includes all the vertices of the original graph.

Planer Graph

Graphs that can be drawn on a plane without edge crossings

Incident

Two edges that share a vertex

Cycle

a closed walk

Walk

a finite list of alternating vertices and connecting edges that begins and ends with a vertex.

connected graph

a graph such that there is a path going from any vertex to any other vertex

Face

a region inside a cycle of edges or the infinite exterior region on the outside of the graph.

Regular Bipartite Graph

a regular graph with the same number of vertices on the left-hand side as the right-hand side.

Matching

a subset of edges in a graph so that each vertex is incident with only one edge

Leaf

a vertex of degree 1 in a tree

Path

a walk with no repeated edges or vertices.

Loop

an edge that has the same vertex for both of its ends.

Graph

set of vertices and a set of edges that join pairs of vertices together.

Vertex Cover

set of vertices so that every vertex in the graph is either adjacent to a vertex or in the graph

Degree

the number of edges that are incident

neighborhood

the set of all vertices connected to a vertex N(A)

Hall's Marriage Theorem

there is a matching of the left-hand vertices into the right-hand vertices if and only if for every subset of left-hand vertices

adjacent

two vertices that share an edge