Extremal Kragujevac Trees with Respect to Randic Energy

Document Type : Research Paper

Author

Department of Science‎, ‎Arak University of Technology‎, ‎Arak‎, ‎Iran

Abstract

‎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.

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References

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Iranian Journal of Mathematical Chemistry
Volume 16, Issue 3
September 2025
Pages 245-255

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