Abstract

This paper investigates Tribonacci cordial labeling on two classes of composite graphs formed from cycles and paths. While Fibonacci-based cordial labeling has been extensively studied, results involving higher-order recurrence sequences, particularly the Tribonacci sequence, remain limited—especially for graphs constructed by combining fundamental structures such as cycles and paths.

Motivated by this gap, we consider two families of graphs, namely G(C_n,C_m,P_k), obtained by connecting two cycle graphs via a path, and G_k(C_n), consisting of multiple cycle graphs sharing a common adjacent vertex. By exploiting the parity properties of the Tribonacci sequence and constructing appropriate injective vertex labelings, we establish that both graph classes admit Tribonacci cordial labeling for all integers n,m≥3,k≥2.

The results highlight the crucial role of the periodic parity pattern of the Tribonacci sequence in achieving balanced edge labelings and extend existing studies on Fibonacci cordial labeling to higher-order recurrence sequences. Several illustrative examples are provided to demonstrate the proposed constructions.

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