- the key elements of a graph or network (vertex, edge, face, loop, degree of a vertex, weight, direction);
- different forms of representation of graphs (edge and vertex sets, network diagrams, matrices);
- types of graphs (simple, planar, connected, complete, tree, bi-partite, directed graph);
- subgraphs of graphs (spanning trees, eulerian and hamiltonian paths and circuits);
- key theorems and algorithms (network flow, minimum spanning tree, assignment, allocation, critical path).
- draw and modify graphs according to given specifications;
- model applications in a variety of contexts using various representations of graphs as networks;
- identify particular characteristics of graphs, carry out constructions on graphs and calculate various measures related to graphs;
- use algorithms such as forward and backward scanning, ‘minimum cut-maximum flow’, prim’s and hungarian algorithms, and ‘crashing’ as applicable, to optimise associated characteristics in given contexts.
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