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Mathematics and Statistics Vol. 13(4), pp. 194 - 200
DOI: 10.13189/ms.2025.130402
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-Fibonacci Cordial Labeling to Create New -Fibonacci Cordial Families

R. Charishma , P. Nageswari ^*
Department of Mathematics, Noorul Islam Centre for Higher Education, Kumaracoil, Tamil Nadu, India

ABSTRACT

Cordial labeling is a pivotal concept in graph theory, involving assigning labels to graph elements to satisfy specific balance conditions. While traditional cordial labelings use binary or integer labels, this research introduces -Fibonacci Cordial labeling, a novel approach integrating Fibonacci sequences, a cornerstone of combinatorial mathematics into graph labeling. This research investigated the -Fibonacci Cordial labeling for path, cycle, Petersen graph, -pan graph and Bistar graph. The Fibonacci numbers are determined by the linear recurrence relations which output an endless list of integers = 0, 1, 1, 2, 3, 5, 8, 13, 21, 34, 55, 89, 144, … for = 0, 1, 2, 3, …, 12, … An injective function from vertices of to where denotes the Fibonacci number (=1, 1, 2,…,n) is said to be -Fibonacci Cordial labeling of if the induced function g* is a function from edges of to {0,1}. This results in edge labeled as 0 if the maximum label among the two adjacent vertices is an even number and 1 otherwise satisfies the condition number of vertices labeled with 0 and 1 differed by atmost 1. A graph admits -Fibonacci Cordial Labeling is called -Fibonacci Cordial Graph. The research demonstrates that paths, cycles, and Bistar graphs successfully admit -Fibonacci Cordial labeling. The Petersen graph and pan graph require tailored labeling strategies due to their complex symmetries but are shown to comply with the balance condition. Fibonacci sequences introduce unique structural constraints, enabling novel insights into graph connectivity and label distribution. This paper examines the -Fibonacci cordial labeling of various graphs. It provides explicit labeling schemes for key graph classes, serving as a foundation for future research in cryptographic algorithms, network design, and error-correcting codes.

KEYWORDS
-Fibonacci Cordial Labeling; -Fibonacci Cordial Graph, -Fibonacci Petersen Graph, Bistar, -pan Graph

Cite This Paper in IEEE or APA Citation Styles
(a). IEEE Format:
[1] R. Charishma , P. Nageswari , "-Fibonacci Cordial Labeling to Create New -Fibonacci Cordial Families," Mathematics and Statistics, Vol. 13, No. 4, pp. 194 - 200, 2025. DOI: 10.13189/ms.2025.130402.

(b). APA Format:
R. Charishma , P. Nageswari (2025). -Fibonacci Cordial Labeling to Create New -Fibonacci Cordial Families. Mathematics and Statistics, 13(4), 194 - 200. DOI: 10.13189/ms.2025.130402.