Maximum randć energy of unicyclic graphs

Articles in Press

Document Type : Research Paper

Authors

1 Department of Mathematics, Shahed University, Tehran, Iran.

2 Department of Mathematics, Azarbaijan Shahid Madani University, Tabriz, Iran.

Abstract

Given a graph $ G = (V, E) $, the randć   matrix of $G$ is $ R(G) = (r_{ij}) $, where $r_{ij}=\frac{1}{\sqrt{d_{v_i}d_{v_j}}}$ if $v_iv_j \in E(G)$ and $0$ otherwise, and $ d_{v_i}$ is the degree of the vertex $ v_{i} $ in $ G$. The randć  energy is the sum of absolute values of the eigenvalues of randć  matrix. The $R$-polynomial of $ G $ is defined by $ \phi_{R} (G, x)=det(xI_{n}-R(G)) $. In this paper, we obtain the $R$-polynomial as well as the randć  energy of a unicyclic graph. In particular, we determine all unicyclic graphs with maximum randć  energy.

Keywords

References

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Algebraic Structures and Their Applications

Articles in Press, Corrected Proof
Available Online from 12 October 2025

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