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General Mathematics
Graphs and networks
Chapter 7
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Build the connection matrix of a network
CH 4
Vertices, edges and degree
Connected graphs, bridges and isomorphism
Euler's formula
Walks and paths
Eulerian trails and circuits
Hamiltonian paths and cycles
Weighted graphs and shortest paths
Trees and minimum spanning trees
Count the vertices, edges and loops of a displayed graph
Determine the degree of a named vertex and classify it as even or odd
Use sum of degrees = 2 × edges in both directions
Decide whether a graph is connected and identify separated groups
Identify the bridge or bridges of a connected graph
Decide whether two graphs are isomorphic by checking their structure
Distinguish planar form from the property of being planar
State the number of faces of a connected planar graph in planar form
Verify and solve v + f = e + 2 for a connected planar graph
Check whether a listed vertex sequence is a walk on a graph
Classify a valid walk as a trail, path, circuit or cycle
Decide whether a graph has an Eulerian trail, circuit, both or neither
Verify whether a listed route is an Eulerian trail or circuit
Verify whether a listed route is a Hamiltonian path or cycle
Read an edge weight and total the length of a stated route
Find the shortest path between two vertices by inspection
Decide whether a graph or subgraph is a tree
Identify a spanning tree and compute its length
Determine a minimum spanning tree and its total weight
Recognise what a greedy algorithm is and where it applies