CAS MA 109 Lecture Notes - Lecture 2: Eulerian Path
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11 Sep 2017
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Collection of dots called nodes and a collection of curves that start and end at nodes. Nodes are sometimes called vertices and the network, graphs. List of edges such that each edge of the list ends at a node where the next edge begins. Starting at node 1, abacgfbe is a path. A path that starts and ends at the same node. Starting at node 1, abacge is a circuit. A circuit that uses each edge of the graph exactly once (so a path that starts and ends at the same node that uses each edge exactly once) Number of edges that start or end at that node. Therefore, if a network has an euler circuit, then every node that is not the start = end node must have even degree. Conjecture: if a network has an euler circuit, then the degree of every node of the network must be an even number.
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