MATH1180 Lecture Notes - Lecture 1: Eulerian Path

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A graph consists of a finite set of points, called verities, and lines, called edges, that join a pair of vertices. A vertex of a graph is odd if it is an endpoint of an odd number of edges of a graph. A vertex is even if it is an endpoint of an even number of edges. A graph is connected if it is possible to travel from any vertex to any other vertex of the graph by moving along successive edges. A bridge in a connected graph is an edge such that if it were removed, the graph is no longer connected: connected graphs are called networks. A path in a graph is a series of consecutive edges in which no edge is repeated. The number of edges in a path is called its length. A path containing all the edges of a graph is called a euler path.

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