Further Results on Bijective Product k -Cordial Labeling

Sabah A. Bashammakh, Wai Chee Shiu, Robinson Santrin Sabibha, Pon Jeyanthi () and Mohamed Elsayed Abdel-Aal
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Sabah A. Bashammakh: Department of Mathematics and Statistics, Faculty of Science, University of Jeddah, P.O. Box 80327, Jeddah 21589, Saudi Arabia
Wai Chee Shiu: Department of Mathematics, The Chinese University of Hong Kong, Shatin, Hong Kong, China
Robinson Santrin Sabibha: Department of Science and Humanities, Vins Christian College of Engineering, Nagercoil 629807, Tamilnadu, India
Pon Jeyanthi: Research Centre, Department of Mathematics, Govindammal Aditanar College for Women, Tiruchendur 628215, Tamilnadu, India
Mohamed Elsayed Abdel-Aal: Department of Mathematics, Faculty of Science, Banha University, Banha 13518, Egypt

Mathematics, 2025, vol. 13, issue 15, 1-12

Abstract: A bijective product k -cordial labeling f of a graph G with vertex set V and edge set E is a bijection from V to { 1 , 2 , … , | V | } such that the induced edge labeling f × : E ( G ) → Z k = { i | 0 ≤ i ≤ k − 1 } defined as f × ( u v ) ≡ f ( u ) f ( v ) ( mod k ) for every edge u v ∈ E satisfies the condition | e f × ( i ) − e f × ( j ) | ≤ 1 , where i , j ∈ Z k and e f × ( i ) is the number of edges labeled with i under f × . A graph which admits a bijective product k -cordial labeling is called a bijective product k -cordial graph. In this paper, we study bijective product π -cordiality for paths and cycles, where π is an odd prime. We determine bijective product π -cordiality for paths and cycles for 3 ≤ π ≤ 13 . Also, we establish the bijective product k -cordial labeling of stars. Further, we find the bijective product 4-cordial labeling of bistars and the splitting graphs of stars and bistars.

Keywords: cordial labeling; product cordial labeling; k-product cordial labeling; bijective product k-cordial labeling (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2025
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