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K-Product Cordial Labeling of Powers of Paths

K. Jeya Daisy (1), R. Santrin Sabibha (2), P. Jeyanthi (3) and Maged Z. Youssef (4)

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

Email address: jeyadaisy@yahoo.com

 

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

Email address: sanithazhi@gmail.com

 

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

Email address: jeyajeyanthi@rediffmail.com

 

(4) 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

Email address: mzyoussef11566@yahoo.com

Doi : https://doi.org/10.47013/15.4.8

Cited by : Jordan J. Math & Stat., 15 (4A) (2022), 911 - 924

PDF

Received on: June 8, 2021;                                           Accepted on: April 14, 2022

 Abstract. Let f be a map from V (G) to {0, 1, ..., k − 1}, where k is an integer and 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 ϵ {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). In this paper, we add some new results on k-product cordial labeling and prove that the graph P2n is 4-product cordial. Further, we study the k-product cordial behaviour of powers of paths P3n, P4n and P5n for k = 3 and 4.

Keywords: cordial labeling, product cordial labeling, k-product cordial labeling, 3-product cordial labeling, 4-product cordial labeling.