Signed degree sets in signed graphs

Shariefuddin Pirzada; T. A. Naikoo; F. A. Dar

Czechoslovak Mathematical Journal (2007)

  • Volume: 57, Issue: 3, page 843-848
  • ISSN: 0011-4642

Abstract

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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.

How to cite

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Pirzada, Shariefuddin, Naikoo, T. A., and Dar, F. A.. "Signed degree sets in signed graphs." Czechoslovak Mathematical Journal 57.3 (2007): 843-848. <http://eudml.org/doc/31166>.

@article{Pirzada2007,
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.},
author = {Pirzada, Shariefuddin, Naikoo, T. A., Dar, F. A.},
journal = {Czechoslovak Mathematical Journal},
keywords = {signed graphs; signed degree set},
language = {eng},
number = {3},
pages = {843-848},
publisher = {Institute of Mathematics, Academy of Sciences of the Czech Republic},
title = {Signed degree sets in signed graphs},
url = {http://eudml.org/doc/31166},
volume = {57},
year = {2007},
}

TY - JOUR
AU - Pirzada, Shariefuddin
AU - Naikoo, T. A.
AU - Dar, F. A.
TI - Signed degree sets in signed graphs
JO - Czechoslovak Mathematical Journal
PY - 2007
PB - Institute of Mathematics, Academy of Sciences of the Czech Republic
VL - 57
IS - 3
SP - 843
EP - 848
AB - 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.
LA - eng
KW - signed graphs; signed degree set
UR - http://eudml.org/doc/31166
ER -

References

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  1. On signed degrees in signed graphs, Czech. Math. J. 44 (1994), 677–690. (1994) MR1295143
  2. 10.1137/0110037, SIAM J. Appl. Math. 10 (1962), 496–506. (1962) MR0148049DOI10.1137/0110037
  3. 10.1307/mmj/1028989917, Michigan Math. J. 2 (1953), 143–146. (1953) MR0067468DOI10.1307/mmj/1028989917
  4. Degree sets for graphs, Fund. Math. 65 (1977), 189–194. (1977) MR0480200
  5. 10.1002/(SICI)1097-0118(199710)26:2<111::AID-JGT6>3.0.CO;2-V, J. Graph Theory 26 (1997), 111–117. (1997) MR1469358DOI10.1002/(SICI)1097-0118(199710)26:2<111::AID-JGT6>3.0.CO;2-V

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