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Signed degree sets in signed graphs

Shariefuddin PirzadaT. A. NaikooF. A. Dar — 2007

Czechoslovak Mathematical Journal

The set D of distinct signed degrees of the vertices in a signed graph G is called its signed degree set. In this paper, we prove that every non-empty set of positive (negative) integers is the signed degree set of some connected signed graph and determine the smallest possible order for such a signed graph. We also prove that every non-empty set of integers is the signed degree set of some connected signed graph.

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