Show that every graph with two or more nodes contains two nodes that have equal degrees
Problem: The above claim is not completely true if self-loops are allowed. What should I do?
Graph Theory Proof involving vertex degree
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graph-theory
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2complain, maybe? – 2017-01-11
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0Just kidding, you should probably assume they aren't allowed and try the problem, then complain. – 2017-01-11
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0Not just loops, also multiple edges cause problems: you can draw a graph with three nodes of degrees one, two, and three. Also, there are infinite graphs in which no two nodes have the same degree. You need to assume a ***finite simple graph***. – 2017-01-11
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0Sometimes graphs without self loops are called *simple*, but other times undirected graphs are just assumed to be simple. – 2017-01-11