| Title:
|
Signed degree sets in signed graphs (English) |
| Author:
|
Pirzada, S. |
| Author:
|
Naikoo, T. A. |
| Author:
|
Dar, F. A. |
| Language:
|
English |
| Journal:
|
Czechoslovak Mathematical Journal |
| ISSN:
|
0011-4642 (print) |
| ISSN:
|
1572-9141 (online) |
| Volume:
|
57 |
| Issue:
|
3 |
| Year:
|
2007 |
| Pages:
|
843-848 |
| Summary lang:
|
English |
| . |
| Category:
|
math |
| . |
| Summary:
|
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. (English) |
| Keyword:
|
signed graphs |
| MSC:
|
05C07 |
| MSC:
|
05C20 |
| MSC:
|
05C22 |
| idZBL:
|
Zbl 1174.05059 |
| idMR:
|
MR2356284 |
| . |
| Date available:
|
2009-09-24T11:49:53Z |
| Last updated:
|
2020-07-03 |
| Stable URL:
|
http://hdl.handle.net/10338.dmlcz/128210 |
| . |
| Reference:
|
[1] G. Chartrand, H. Gavlas, F. Harary and M. Schultz: On signed degrees in signed graphs.Czech. Math. J. 44 (1994), 677–690. MR 1295143 |
| Reference:
|
[2] 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. MR 0148049, 10.1137/0110037 |
| Reference:
|
[3] F. Harary: On the notion of balance in a signed graph.Michigan Math. J. 2 (1953), 143–146. MR 0067468, 10.1307/mmj/1028989917 |
| Reference:
|
[4] S. F. Kapoor, A. O. Polimeni and C. E. Wall: Degree sets for graphs.Fund. Math. 65 (1977), 189–194. MR 0480200 |
| Reference:
|
[5] 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. MR 1469358, 10.1002/(SICI)1097-0118(199710)26:2<111::AID-JGT6>3.0.CO;2-V |
| . |
