| Title:
|
On prime labeling of union of tadpole graphs (English) |
| Author:
|
Patel, Sanjaykumar K. |
| Author:
|
Vasava, Jayesh B. |
| Language:
|
English |
| Journal:
|
Commentationes Mathematicae Universitatis Carolinae |
| ISSN:
|
0010-2628 (print) |
| ISSN:
|
1213-7243 (online) |
| Volume:
|
63 |
| Issue:
|
1 |
| Year:
|
2022 |
| Pages:
|
33-50 |
| Summary lang:
|
English |
| . |
| Category:
|
math |
| . |
| Summary:
|
A graph $G$ of order $n$ is said to be a prime graph if its vertices can be labeled with the first $n$ positive integers in such a way that the labels of any two adjacent vertices in $G$ are relatively prime. If such a labeling on $G$ exists then it is called a prime labeling. In this paper we seek prime labeling for union of tadpole graphs. We derive a necessary condition for the existence of prime labelings of graphs that are union of tadpole graphs and further show that the condition is also sufficient in case of union of two or three tadpole graphs. (English) |
| Keyword:
|
prime labeling |
| Keyword:
|
tadpole graph |
| Keyword:
|
union of graphs |
| MSC:
|
05C78 |
| idZBL:
|
Zbl 07584112 |
| idMR:
|
MR4445736 |
| DOI:
|
10.14712/1213-7243.2022.009 |
| . |
| Date available:
|
2022-07-18T11:49:18Z |
| Last updated:
|
2024-04-01 |
| Stable URL:
|
http://hdl.handle.net/10338.dmlcz/150426 |
| . |
| Reference:
|
[1] Fu H.-L, Huang K. C.: On prime labellings.Discrete Math. 127 (1994), no. 1–3, 181–186. MR 1273601, 10.1016/0012-365X(92)00477-9 |
| Reference:
|
[2] Gallian J. A.: A dynamic survey of graph labeling.Electron. J. Combin. 5 (1998), Dynamic Survay 6, 43 pages. MR 1668059 |
| Reference:
|
[3] Kim S.-R., Park J. Y.: On super edge-magic graphs.Ars Combin. 81 (2006), 113–127. MR 2267806 |
| Reference:
|
[4] Klee S., Lehmann H., Park A.: Prime labeling of families of trees with Gaussian integers.AKCE Int. J. Graphs Combin. 13 (2016), no. 2, 165–176. MR 3560568, 10.1016/j.akcej.2016.04.001 |
| Reference:
|
[5] Patel S. K., Shrimali N. P.: Neighborhood-prime labeling of some product graphs.Algebra Discrete Math. 25 (2018), no. 1, 118–129. MR 3798298 |
| Reference:
|
[6] Patel S. K., Vasava J.: On prime labeling of some union graphs.Kragujevac J. Math. 42 (2018), no. 3, 441–452. MR 3856509, 10.5937/KgJMath1803441P |
| Reference:
|
[7] Tout R., Dabboucy A. N., Howalla K.: Prime labeling of graphs.Nat. Acad. Sci. Lett. 11 (1982), 365–368. |
| Reference:
|
[8] Truszczyński M.: Graceful unicyclic graphs.Demonstratio Math. 17 (1984), no. 2, 377–387. MR 0771559 |
| . |
