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Friday, February 5, 2010

The Handshaking Lemma ( First steps in Graph Theory )

Beginning Graph Theory is basically learning new words. I once heard that the Eskimo's have over one hundred  words for snow. It looks as though mathematicians have as many words for graphs. Graph, regular graph, null graph, complete graph, labelled graph, unlabelled graph, subgraph, cycle graph and this is only the beginning. The first theorem in Graph Theory is called 'The Handshaking Lemma'.
In any graph the sum of all the vertex degrees is equal to twice the number of edges.

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(Raumpatrouille – Die phantastischen Abenteuer des Raumschiffes Orion, colloquially aka Raumpatrouille Orion was the first German science fiction television series. Its seven episodes were broadcast by ARD beginning September 17, 1966. The series has since acquired cult status in Germany. Broadcast six years before Star Trek first aired in West Germany (in 1972), it became a huge success.)