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.
This is a preview of subscription content, log in via an institution to check access.
Similar content being viewed by others
References
G. Chartrand, H. Gavlas, F. Harary and M. Schultz: On signed degrees in signed graphs. Czech. Math. J. 44 (1994), 677–690.
S. L. Hakimi: On the realizability of a set of integers as degrees of the vertices of a graph. SIAM J. Appl. Math. 10 (1962), 496–506.
F. Harary: On the notion of balance in a signed graph. Michigan Math. J. 2 (1953), 143–146.
S. F. Kapoor, A.O. Polimeni and C.E. Wall: Degree sets for graphs. Fund. Math. 65 (1977), 189–194.
J. H. Yan, K.W. Lih, D. Kuo and G. J. Chang: Signed degree sequences of signed graphs. J. Graph Theory 26 (1997), 111–117.
Author information
Authors and Affiliations
Rights and permissions
About this article
Cite this article
Pirzada, S., Naikoo, T.A. & Dar, F.A. Signed degree sets in signed graphs. Czech Math J 57, 843–848 (2007). https://doi.org/10.1007/s10587-007-0079-z
Received:
Issue Date:
DOI: https://doi.org/10.1007/s10587-007-0079-z