University of Kashan Iranian Journal of Mathematical Chemistry 2228-6489 16 3 2025 09 01 Extremal Kragujevac Trees with Respect to Randic Energy 245 255 115049 10.22052/ijmc.2025.255399.1897 EN Abbas Heydari Department of Science‎, ‎Arak University of Technology‎, ‎Arak‎, ‎Iran Journal Article 2024 09 11 ‎Let $G$ be a simple graph with vertex set $V(G)=\{v_1‎, ‎v_2‎,‎\dots,v_n\}$‎. ‎The Randi\'c matrix of G‎, ‎represented as R(G)‎, ‎is‎ defined as the $n \times n$ matrix whose $(i‎, ‎j)$-entry is‎ $(d_id_j)^{\frac{-1}{2}}$‎ ‎if $v_i$ and $v_j$ are adjacent and 0 otherwise‎. ‎The Randi\'c energy of graph G is the sum of absolute values of the‎ ‎eigenvalues of R(G)‎. ‎In this study‎, ‎we determine the Kragujevac trees with a fixed degree and fixed order that have maximal and minimal Randić energy‎. Additionally‎, ‎we obtain upper and lower bounds for the Randić energy of these trees‎. https://ijmc.kashanu.ac.ir/article_115049_4520730b7dda4a6eba46bade40267db2.pdf