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Show that a graph without isolated vertices has an Eulerian walk if and only if it...

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Advance Math

Show that a graph without isolated vertices has an Eulerian walkif and only if it is connected and all vertices except at most twohave even degree.

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Prove If an undirected graph G has an Eulerian walk W the graph can have at most two odd degree vertices For a vertex v let dv be the degree of v and let nWv be the number of edges on W incident to v Since W is Eulerian nWv dv Also observe that nWv must be even for all vertices other than the start and end vertices of the W This is because each time W enters an intermediate vertex it must exit it so W    See Answer
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