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Ch03 Graph Theory 1s09 - Chapter 3 Topology Topology is a...

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Fundamentals of Graph Fundamentals of Graph Theory Theory Chapter 3 Artemio P. Magabo Artemio P. Magabo Professor of Electrical Engineering Department of Electrical and Electronics Engineering University of the Philippines - Diliman Department of Electrical and Electronics Engineering Topology Topology is a branch of geometry that concerns with the properties of a geometric figure that are not changed when the figure is twisted, bent, folded, stretched or tied in knots, provided that no parts of the figure are cut apart or joined together. A graph is a picture of an electric circuit where each element has been replaced by a line segment. 3 Ω 4V + - 2A + - V x + - 5V x 1 Ω 2 Ω Department of Electrical and Electronics Engineering Definitions Node – a point of connection of two or more elements Path - a set of elements that may be traversed in order without passing through the same node twice Branch - a single path, containing one simple element, which connects one node to another node Loop - a closed path Mesh - a loop which does not contain any other loop within it Department of Electrical and Electronics Engineering Sub-graph – the graph formed after some branches are removed from the original graph Planar Graph - a graph which may be drawn on a plane surface in such a way that no branch passes over or under any other branch Non-planar Graph - a graph which is not planar These planar graphs are topologically equivalent. d b c a c b d a a c d b n=4 b=6
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Department of Electrical and Electronics Engineering n=6 b=9 This graph is non-planar. n=5 b=9 This graph is planar. Department of Electrical and Electronics Engineering Tree - a subgraph with the following properties: 1. It contains all the nodes of the original graph. No node is left in isolation.
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