Graphs and Networks

Identify elements of a graph including dots, vertices, edges, loops and faces

Determine the degree of a vertex

Demonstrate the meaning of, and use, the terms: subgraph, simple graph, complete graph, bipartite graph, digraph, arc, weighted graph and network

Identify isomorphic graphs

Identify connected graphs and bridges

Redraw a graph in planar form

Identify planar graphs

Using Euler's formula to determine element values of a connected planar graph

Verify Euler's rule given a connected planar graph

Construct an adjacency matrix

Construct a graph from an adjacency matrix

Reading a graph to write down the list of vertices in order of a walk, trail, path, circuit or cycle

Identify traversable graphs

Identify and describe the movement around a graph as a walk, trail, path, circuit or cycle

Investigate the Konigsberg bridge problem

Identify eulerian trails and circuits

Application of eulerian trails and circuits to contextual problems

Identify hamiltonian paths and cycles

Application of hamiltonian paths and cycles to contextual problems

Identify weighted graphs and networks

Finding the shortest path through a network by inspection

Finding the shortest path through a network by Dijkstra's algorithm