### Signed degree sets in signed graphs [article]

S. Pirzada, T. A. Naikoo, F. A. Dar
<span title="2006-09-05">2006</span> <i > arXiv </i> &nbsp; <span class="release-stage" >pre-print</span>
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.
<span class="external-identifiers"> <a target="_blank" rel="external noopener" href="https://arxiv.org/abs/math/0609121v1">arXiv:math/0609121v1</a> <a target="_blank" rel="external noopener" href="https://fatcat.wiki/release/2kv2nl4bdjf7vjuus7tnv42eyq">fatcat:2kv2nl4bdjf7vjuus7tnv42eyq</a> </span>
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