NOTES ON GRAPH THEORY
You need to know these terms
NODE or VERTEX
ARC or EDGE
A route or trail is a sequence of arcs and nodes
PRTSR is such an example. (Note R appears twice)
A path is a finite sequence of arcs (or edges) where no arc is used more than once
PQRS is such a path
R
S
P
T
U
Q
A cycle
A closed path.
Starts and ends at the same node
(The end node of the last arc/edge is the starting node of the first arc)
A subgraph
A diagram which represents elements or parts of another graph
A simple graph
Every node is simply connected to other nodes (no duplicated arcs or loops etc..)
The degree or ORDER of a node (or vertex)
The number of arcs meeting at that node
A complete graph
EVERY node is connected to every other node by EXACTLY ONE arc
A directed graph (digraph)
A graph with arrows that denote direction within a network
A bipartite graph
Two sets of nodes that are connected by arcs
A Eulerian graph
A connected graph which has a CLOSED trail that includes EVERY ARC EXACTLY ONCE
A SEMI- Eulerian graph
A connected graph that includes EVERY ARC EXACTLY ONCE but NOT CLOSED.
A planar graph
A graph where arcs do not cross other arcs eg. Corners (nodes) and edges (arcs) of a cube.
A tree
A connected graph that has no cycles
A spanning tree
Any connected graph has at least one sub-graph which is a TREE connecting every node of the original graph.
Puzzle
Can you represent this puzzle as a series of nodes and arc? Use the space below