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Graph Theory
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Key Concepts:
Terms in this set (14)
Connected Graph
One which every vertex is linked by an edge or sequence of edges to every other vertex
Simple Graph
One which there are no loops and two vertices are connected directly by at most only one edge
Subgraph
A graph that exists within a graph using some of the vertices and nodes.
Total Degree of a network
2*number of edges
Trees
A tree is a connected graph with one less edge than the number of nodes. In a tree graph all nodes are connected and there is only one route between each vertex
Eularian Network
Where all the vertices have an even order
Semi-eularian network
Only 2 vertices with an odd degree
Non-eularian
Has more than 2 edges with an odd degree
Eularian Trail
A trail that uses all edges of a graph
Closed Eularian Trail
A Eularian trail that which starts and finishes at the same vertex
Hamiltonian Graph
A path that visits every node once and returns to the starting node
Complete Graph
One where every vertex is connected directly to every other vertex
Number of edges in a complete graph
1/2n(n-1)
Hamiltonian Cycles formula
1/2(n-1)!
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