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