@article{article_1080426, title={Coefficients of Randic and Sombor characteristic polynomials of some graph types}, journal={Communications Faculty of Sciences University of Ankara Series A1 Mathematics and Statistics}, volume={71}, pages={778–790}, year={2022}, DOI={10.31801/cfsuasmas.1080426}, author={Oz, Mert Sinan}, keywords={Graphs, Randic matrix, Sombor matrix, paths, cycles, adjacency}, abstract={Let <span class="MathJax_Preview" style="color:inherit;"> </span> <span class="mjx-chtml MathJax_CHTML" style="font-size:123%;"> <span class="mjx-math"> <span class="mjx-mrow"> <span class="mjx-mi"> <span class="mjx-char MJXc-TeX-math-I" style="padding-top:.503em;padding-bottom:.316em;">G </span> </span> </span> </span> <span class="MJX_Assistive_MathML">G </span> </span> be a graph. The energy of <span class="MathJax_Preview" style="color:inherit;"> </span> <span class="mjx-chtml MathJax_CHTML" style="font-size:123%;"> <span class="mjx-math"> <span class="mjx-mrow"> <span class="mjx-mi"> <span class="mjx-char MJXc-TeX-math-I" style="padding-top:.503em;padding-bottom:.316em;">G </span> </span> </span> </span> <span class="MJX_Assistive_MathML">G </span> </span> is defined as the summation of absolute values of the eigenvalues of the adjacency matrix of <span class="MathJax_Preview" style="color:inherit;"> </span> <span class="mjx-chtml MathJax_CHTML" style="font-size:123%;"> <span class="mjx-math"> <span class="mjx-mrow"> <span class="mjx-mi"> <span class="mjx-char MJXc-TeX-math-I" style="padding-top:.503em;padding-bottom:.316em;">G </span> </span> </span> </span> <span class="MJX_Assistive_MathML">G </span> </span>. It is possible to study several types of graph energy originating from defining various adjacency matrices defined by correspondingly different types of graph invariants. The first step is computing the characteristic polynomial of the defined adjacency matrix of <span class="MathJax_Preview" style="color:inherit;"> </span> <span class="mjx-chtml MathJax_CHTML" style="font-size:123%;"> <span class="mjx-math"> <span class="mjx-mrow"> <span class="mjx-mi"> <span class="mjx-char MJXc-TeX-math-I" style="padding-top:.503em;padding-bottom:.316em;">G </span> </span> </span> </span> <span class="MJX_Assistive_MathML">G </span> </span> for obtaining the corresponding energy of <span class="MathJax_Preview" style="color:inherit;"> </span> <span class="mjx-chtml MathJax_CHTML" style="font-size:123%;"> <span class="mjx-math"> <span class="mjx-mrow"> <span class="mjx-mi"> <span class="mjx-char MJXc-TeX-math-I" style="padding-top:.503em;padding-bottom:.316em;">G </span> </span> </span> </span> <span class="MJX_Assistive_MathML">G </span> </span>. In this paper, formulae for the coefficients of the characteristic polynomials of both the Randic and the Sombor adjacency matrices of path graph <span class="MathJax_Preview" style="color:inherit;"> </span> <span class="mjx-chtml MathJax_CHTML" style="font-size:123%;"> <span class="mjx-math"> <span class="mjx-mrow"> <span class="mjx-msubsup"> <span class="mjx-base" style="margin-right:-.109em;"> <span class="mjx-mi"> <span class="mjx-char MJXc-TeX-math-I" style="padding-top:.441em;padding-bottom:.253em;padding-right:.109em;">P </span> </span> </span> <span class="mjx-sub" style="font-size:70.7%;vertical-align:-.212em;padding-right:.071em;"> <span class="mjx-mi"> <span class="mjx-char MJXc-TeX-math-I" style="padding-top:.191em;padding-bottom:.316em;">n </span> </span> </span> </span> </span> </span> <span class="MJX_Assistive_MathML">Pn </span> </span> , cycle graph <span class="MathJax_Preview" style="color:inherit;"> </span> <span class="mjx-chtml MathJax_CHTML" style="font-size:123%;"> <span class="mjx-math"> <span class="mjx-mrow"> <span class="mjx-msubsup"> <span class="mjx-base" style="margin-right:-.045em;"> <span class="mjx-mi"> <span class="mjx-char MJXc-TeX-math-I" style="padding-top:.503em;padding-bottom:.316em;padding-right:.045em;">C </span> </span> </span> <span class="mjx-sub" style="font-size:70.7%;vertical-align:-.212em;padding-right:.071em;"> <span class="mjx-mi"> <span class="mjx-char MJXc-TeX-math-I" style="padding-top:.191em;padding-bottom:.316em;">n </span> </span> </span> </span> </span> </span> <span class="MJX_Assistive_MathML">Cn </span> </span> are presented. Moreover, we obtain the five coefficients of the characteristic polynomials of both Randic and Sombor adjacency matrices of a special type of 3−regular graph <span class="MathJax_Preview" style="color:inherit;"> </span> <span class="mjx-chtml MathJax_CHTML" style="font-size:123%;"> <span class="mjx-math"> <span class="mjx-mrow"> <span class="mjx-msubsup"> <span class="mjx-base"> <span class="mjx-mi"> <span class="mjx-char MJXc-TeX-math-I" style="padding-top:.441em;padding-bottom:.316em;">R </span> </span> </span> <span class="mjx-sub" style="font-size:70.7%;vertical-align:-.212em;padding-right:.071em;"> <span class="mjx-mi"> <span class="mjx-char MJXc-TeX-math-I" style="padding-top:.191em;padding-bottom:.316em;">n </span> </span> </span> </span> </span> </span> <span class="MJX_Assistive_MathML">Rn </span> </span>.}, number={3}, publisher={Ankara University}