A-Level Definitions Flashcards
(13 cards)
Define the term graph.
A graph G consists of points (vertices or nodes) which are connected by lines (edges or arcs)
Define the term subgraph.
A subgraph of G is a graph, each of whose vertices belongs to G and each of whose edges belongs to G
Define the term degree or valency.
The degree or valency of a vertex is the number of edges incident to it. A vertex is odd (even) if it has odd
(even) degree
Define the term path.
A path is a finite sequence of edges, such that the end vertex of one edge in the sequence is the start vertex
of the next, and in which no vertex appears more then once.
Define the term cycle/circuit.
A cycle (circuit) is a closed path, ie the end vertex of the last edge is the start vertex of the first edge.
Define the term connected.
Two vertices are connected if there is a path between them. A graph is connected if all its vertices are
connected.
Define the term tree.
A tree is a connected graph with no cycles
Define the term spanning tree.
A spanning tree of a graph G is a subgraph which includes all the vertices of G and is also a tree.
Define the term minimum spanning tree.
A minimum spanning tree (MST) is a spanning tree such that the total length of its arcs is as small as
possible. (MST is sometimes called a minimum connector.)
Define the term complete graph.
A graph in which each of the n vertices is connected to every other vertex is called a complete graph.
Define the term bipartite graph.
A bipartite graph consists of two sets of vertices X and Y. The edges only join vertices in X to vertices in Y,
not vertices within a set. (If there are r vertices in X and s vertices in Y then this graph is Kr,s.)
Define the term matching.
A matching is the pairing of some or all of the elements of one set, X, with elements of a second set, Y. If
every member of X is paired with a member of Y the matching is said to be a complete matching.
Define the term directed graphs.
If the edges of a graph have a direction associated with them they are known as directed edges and the graph
is known as a digraph.
