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  3. a point v of degree 0 is called an isolated point

A point v of degree 0 is called an isolated point A point v of...

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Calculus

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A point v of degree 0 is called an isolated point A point v of degree one is called an end point Note Loops are counted twice Example Consider the following 4 5 graph Fig 1 13 1 3 Fig 1 13 d 1 2 d 2 4 d 3 2 d 4 2 Total degrees 10 2 x 5 Theorem 1 1 The sum of the degrees of the points of a graph G is twice the number of lines in G i e Ed vi 2q Proof Every line of G is incident with two points Every line contributes two degrees There are q lines in p q graph 1d v 2q 2x number of lines in G Theorem 1 2 In any group G the number of points of odd degree is even Proof Let V V2 V denote the points of odd degree and w W Wm denote the points of even degree in G By theorem 1 1 1 d v 1 d w 2 q which is even

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