In this paper, we introduce the concept of balanced triclique polynomial and balanced triclique neighborhood polynomial of graphs. First, we characterize the balanced tricliques in complete graphs of order at least three and complete q-particle graphs for q ≥ 3 Moreover, we establish the corresponding polynomials.

triclique, triclique polynomial, neighborhood system

Received: October 16, 2024; Revised: December 17, 2024; Accepted: January 21, 2025; Published: March 7, 2025

How to cite this article: Mohammad Nur S. Paspasan, Aldison M. Asdain, Eman C. Ahmad and Rosalio G. Artes Jr., Triclique polynomials and triclique neighborhood polynomials of some graphs, Advances and Applications in Discrete Mathematics 42(4) (2025), 335-342. https://doi.org/10.17654/0974165825021

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