Decision 2 0.0 / 5 ? Further MathsRulesA2/A-levelEdexcel Created by: carmen.lauCreated on: 21-06-19 19:52 Euler's handshaking lemma The total of the orders of nodes is x2 the number of arcs 1 of 19 Consequence of Euler's lemma Cannot be an odd number of odd nodes 2 of 19 Bubble sort: max number of comparisons/ swaps 1/2n(n-1) 3 of 19 Connected graph: order of nodes >1 4 of 19 Eulerian: order of nodes All even & connected 5 of 19 Semi- Eulerian: order of nodes 1 pair of odd nodes 6 of 19 Tree: number of arcs n-1 7 of 19 Kn: number of arcs 1/2n(n-1) 8 of 19 MST: number of arcs n-1 9 of 19 Kruskal's Arcs 10 of 19 Prim's Nodes, matrix 11 of 19 Number of times a node is visited Order of node/2 12 of 19 Graphs which cannot be planar K5 , K3,3 13 of 19 When to apply planarity algorithm Graph contains a Hamiltonian cycle 14 of 19 Floyd's v Dijkstra's Floyd's finds the shortest path between any pair of nodes 15 of 19 When is the optimal solution Biggest lower bound < optimal < smallest upper bound 16 of 19 Critical activities: float 0 17 of 19 Choosing pivot column Smallest number in P row 18 of 19 Ratio test Value / Pivot column number, must be smallest 19 of 19
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