Azarbaijan Shahid Madani University Communications in Combinatorics and Optimization 2538-2128 9 2 2024 06 01 Mathematical results on harmonic polynomials 279 295 14660 10.22049/cco.2023.28920.1779 EN Walter Carballosa Department of Mathematics and Statistics, Florida International University, 11200 SW 8th Street, Miami, FL 33199, USA J. E. Nápoles Departamento de Matemáticas, Universidad Nacional de Nordeste, Avenida de la Libertad 5450, 3400 Corrientes, Argentina José M. Rodríguez Departamento de Matemáticas, Universidad Carlos III de Madrid, Avenida de la Universidad 30, 28911 Leganés, Madrid, Spain O. Rosario Facultad de Matemáticas, Universidad Autónoma de Guerrero, Carlos E. Adame No.54, Col. Garita, 39650 Acalpulco Gro., Mexico José M. Sigarreta Facultad de Matemáticas, Universidad Autónoma de Guerrero, Carlos E. Adame No.54, Col. Garita, 39650 Acalpulco Gro., Mexico Journal Article 2023 08 12 The harmonic polynomial was defined in order to understand better the harmonic topological index. Here, we obtain several properties of this polynomial, and we prove that several properties of a graph can be deduced from its harmonic polynomial. Also, we prove that graphs with the same harmonic polynomial share many properties although they are not necessarily isomorphic. https://comb-opt.azaruniv.ac.ir/article_14660_8071a376a70bf0cc79490badada350e3.pdf