Question: This is a graph theory question. Definitions: Graphical Sequence: A sequence of numbers which works as a degree sequence in a graph. Ex, the graphical

This is a graph theory question.

Definitions:

  • Graphical Sequence: A sequence of numbers which works as a degree sequence in a graph.
  • Ex, the graphical sequence of a straight line path of 4 vertices in a straight line path is {1, 2, 2, 1}, or {2, 2, 1, 1}, etc.

Let d1 d2 dn be a list of non-negative integers such that d1 n1, d1 dn 1 and

i=1ndi is even.

Prove that (d1, d2, . . . , dn) is a graphical sequence.

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