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Signed degree sets in signed graphs

Combinatorics 2007-05-23 v1

Abstract

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.

Keywords

Cite

@article{arxiv.math/0609121,
  title  = {Signed degree sets in signed graphs},
  author = {S. Pirzada and T. A. Naikoo and F. A. Dar},
  journal= {arXiv preprint arXiv:math/0609121},
  year   = {2007}
}