Edge k -Product Cordial Labeling of Trees

Jenisha Jeganathan, Maged Z. Youssef, Jeya Daisy Kruz, Jeyanthi Pon (), Wai-Chee Shiu and Ibrahim Al-Dayel
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Jenisha Jeganathan: Research Scholar, Department of Mathematics, Holy Cross College (Autonomous), Nagercoil, Affiliated to Manonmaniam Sundaranar University, Tirunelveli 627012, Tamilnadu, India
Maged Z. Youssef: Department of Mathematics and Statistics, College of Science, Imam Mohammad Ibn Saud Islamic University (IMSIU), Riyadh 11566, Saudi Arabia
Jeya Daisy Kruz: Department of Mathematics, Holy Cross College (Autonomous), Nagercoil 629004, Tamilnadu, India
Jeyanthi Pon: Department of Mathematics, Govindammal Aditanar College for Women, Tiruchendur 628215, Tamilnadu, India
Wai-Chee Shiu: Department of Mathematics, The Chinese University of Hong Kong, Shatin, Hong Kong, China
Ibrahim Al-Dayel: Department of Mathematics and Statistics, College of Science, Imam Mohammad Ibn Saud Islamic University (IMSIU), Riyadh 11566, Saudi Arabia

Mathematics, 2025, vol. 13, issue 21, 1-19

Abstract: The concepts of k -product cordial labeling and edge product cordial labeling were introduced in 2012 and further explored by various researchers. Building on these ideas, we define a new concept called ‘edge k -product cordial labeling’ as follows: For a graph G = ( V ( G ) , E ( G ) ) , which does not have isolated vertices, an edge labeling f : E ( G ) → 0 , 1 , … , k − 1 , where k ≥ 2 is an integer, is said to be an edge k -product cordial labeling of G if it induces a vertex labeling f * : V ( G ) → 0 , 1 , … , k − 1 defined by f * ( v ) = ∏ u v ∈ E ( G ) f ( u v ) ( mod k ) , which satisfies e f ( i ) − e f ( j ) ≤ 1 and v f * ( i ) − v f * ( j ) ≤ 1 for i , j ∈ 0 , 1 , … , k − 1 , where e f ( i ) and v f * ( i ) denote the number of edges and vertices, respectively, having label i for i = 0 , 1 , … , k − 1 . In this paper, we study the edge k -product cordial behavior of trees, a comet, and a double comet.

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