Original Research Article

Article volume = 2024 and issue = 1

Pages: 68–80

Article publication Date: December 09, 2023

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# 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.

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##### 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
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