en تخصصي Special پژوهشي Research paper <p>In the main this paper introduces the concept of chromatic harmonic polynomials denoted, $H^chi(G,x)$ and chromatic harmonic indices denoted, $H^chi(G)$ of a graph $G$. The new concept is then applied to finding explicit formula for the minimum (maximum) chromatic harmonic polynomials and the minimum (maximum) chromatic harmonic index of certain graphs. It is also applied to split graphs and certain derivative split graphs.&nbsp;</p> Chromatic harmonic index, Chromatic harmonic polynomial, Split graph, Derivative split graph 173 184 http://ijmsi.ir/browse.php?a_code=A-10-2373-1&slc_lang=en&sid=1 J. Kok kokkiek2@tshwane.gov.za 10031947532846007815 10031947532846007815 Yes Center for Studies in Discrete Mathematics, Vidya Academy of Science & Technology,Thrissur, India. K. A. Germina srgerminaka@gmail.com 10031947532846007816 10031947532846007816 No Department of Mathematics,School of Physical Sciences, Central University of Kerala, Kasargod, India.