Original Research Article

Article volume = 2024 and issue = 1

Pages: 68–80

Article publication Date: December 09, 2023

You can download PDF file of the article here: Download

Visited 149 times and downloaded 59 times

# k-Product Cordial Labeling of Splitting Graph of Star Graphs

#### K. Jeya Daisya(a), R. Santrin Sabibhab(b), P. Jeyanthi(c), Maged Z. Youssef(d)

(a) Department of Mathematics, Holy Cross College, Nagercoil, Tamilnadu, India.

(b) Research scholar, Register no.: 20212072092001, Manonmaniam Sundaranar University, Tirunelveli, Tamilnadu, India.

(c) Research Centre, Department of Mathematics, Govindammal Aditanar College for Women, Tiruchendur 628215, Tamilnadu, India.

(d) Department of Mathematics and Statistics, College of Science, Imam Mohammad Ibn Saud Islamic University, Riyadh 11623, Saudi

Arabia.

Department of Mathematics, Faculty of Science, Ain Shams University, Abbassia, Cairo, Egypt.

##### Abstract:

Let f be a map from V(G) to {0, 1, ..., k − 1} where k is an integer, 1 ⩽ k ⩽ |V(G)|. For each edge uv assign the label f(u)f(v)(mod k). f is called a k-product cordial labeling if |vf(i) − vf(j)| ⩽ 1, and |ef(i) − ef(j)| ⩽ 1, i, j ∈ {0, 1, ..., k − 1}, where vf(x) and ef(x) denote the number of vertices and edges respectively labeled with x (x = 0, 1, ..., k − 1). A graph that admits k-product cordial labeling is called k-product cordial graph. We have already proved that several families of graphs admit k-product cordial labeling. In this paper, we show that the splitting graph of star graphs admit k-product cordial labeling.

##### Keywords:

cordial labeling, product cordial labeling, k-product cordial labeling, splitting graph, star graph.

##### References:

- [1] I. Cahit, Cordial graphs: a weaker version of graceful and harmonious graphs, Ars Combinatoria, 23(1987), 201–207. 1
- [2] J. A. Gallian, A dynamic survey of graph labeling, The Electronic Journal of Combinatorics, (2022). 1
- [3] F. Harary, Graph Theory, Addison-Wesley, Reading, Massachusetts, (1972). 1
- [4] K. Jeya Daisy, R. Santrin Sabibha, P. Jeyanthi and M. Z. Youssef, k-Product cordial behaviour of union of graphs, Journal of the Indonesian Mathematical Society, Vol. 28, No. 1 (2022), 1–7. 1
- [5] K. Jeya Daisy, R. Santrin Sabibha, P. Jeyanthi and M. Z. Youssef, k-Product cordial labeling of cone graphs, International Journal of Mathematical Combinatorics, Vol. 2 (2022), 72–80. 1
- [6] K. Jeya Daisy, R. Santrin Sabibha, P. Jeyanthi and M. Z. Youssef, k-Product cordial labeling of Napier bridge graphs, Nepal Journal of Mathematical Sciences, Vol. 3, No. 2 (2022), 59–70. 1
- [7] K. Jeya Daisy, R. Santrin Sabibha, P. Jeyanthi and M. Z. Youssef, k-Product cordial labeling of product of graphs, Discrete Mathematics, Algorithms and Applications, Vol. 16, No. 1 (2024), 2250187(8pages), doi: 10.1142/S1793830922501877. 1
- [8] K. Jeya Daisy, R. Santrin Sabibha, P. Jeyanthi and M. Z. Youssef, k-Product cordial labeling of powers of paths, Jordan Journal of Mathematics and Statistics, Vol. 15, No. 4A (2022), 911–924. 1
- [9] K. Jeya Daisy, R. Santrin Sabibha, P. Jeyanthi and M. Z. Youssef, k-Product cordial labeling of fan graphs, TWMS Journal of Applied and Engineering Mathematics, Vol. 13, No. 1 (2023), 11–20. 1
- [10] K. Jeya Daisy, R. Santrin Sabibha, P. Jeyanthi and M. Z. Youssef, Further results on k-product cordial labeling, TWMS Journal of Applied and Engineering Mathematics, in press. 1
- [11] K. Jeya Daisy, R. Santrin Sabibha, P. Jeyanthi and M. Z. Youssef, k-Product cordial labeling of path graphs, preprint. 1
- [12] P. Jeyanthi and A. Maheswari, 3-product cordial labeling of star graphs, Southeast Asian Bulletin of Mathematics, Vol. 39 (2015), 429–437. 1
- [13] R. Ponraj, M. Sivakumar and M. Sundaram, k-product cordial labeling of graphs, International Journal of Contemporary Mathematical Sciences, Vol. 7, No. 15 (2012), 733–742. 1
- [14] A. Rosa, On certain valuations of the vertices of a graph, Theory of Graphs, International Symposium, ICC Rome, (1966), Paris, Dunod (1967), 349–355. 1
- [15] M. Sundaram, R. Ponraj, S. Somasundaram, Product cordial labeling of graphs, Bulletin of Pure and Applied Sciences, 23E(1) (2004), 155–163. 1

##### Cite this article as:

- K. Jeya Daisya, R. Santrin Sabibhab, P. Jeyanthi, Maged Z. Youssef, k-Product Cordial Labeling of Splitting Graph of Star Graphs, Communications in Combinatorics, Cryptography & Computer Science, 2024(1), PP.68–80, 2023
- Export citation to BibTeX