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Unformatted text preview: 8/27/09 11 8/27/09 MATH 224 Discrete Mathematics A spanning tree of a graph is a subgraph that contains all the nodes of a graph and the minimum number of edges to connect the nodes. If the graph has N nodes how many edges will the spanning tree contain? Finding a Minimum Spanning Tree 4 3 1 2 6 5 The six edges in green represent a spanning tree for this graph. 1 2 3 4 5 6 1 1 1 1 1 1 1 1 1 1 1 2 1 1 1 3 1 4 1 1 1 5 1 1 1 1 6 1 1 1 8/27/09 22 8/27/09 MATH 224 Discrete Mathematics A minimum spanning tree of a graph is a subgraph that contains all the nodes of a graph and edges to connect the nodes with minimum cost. Kruskals algorithm selects one edge at a time starting with the smallest and avoiding cycles. Kruskals algorithm is called a greedy algorithm. Finding a Minimum Spanning Tree 4 3 1 2 6 5 1 2 3 4 5 6 5 9 3 2 5 1 5 8 5 3 3 2 9 8 4 3 3 4 2 5 5 5 3 4 5 2 6 5 3 2 5 3 2 3 3 4 8 5 2 5 9 5 8/27/09 33 8/27/09 MATH 224 Discrete Mathematics Select edge {0, 4} and {5, 6} first since they are the smallest.Select edge {0, 4} and {5, 6} first since they are the smallest....
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This note was uploaded on 08/26/2009 for the course MATH 224 taught by Professor Waxman during the Fall '08 term at Southern Illinois University Edwardsville.
 Fall '08
 Waxman
 Math

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