Shahrood University of Technology Journal of Algebraic Systems 2345-5128 14 2 2026 04 01 ON SPECTRA OF HERMITIAN RANDIĆ MATRIX OF SECOND KIND 173 196 3731 10.22044/jas.2024.13993.1787 EN A Bharali Department of Mathematics DIbrugarh University, India Bikash Bhattacharjya Department of Mathematics Indian Institute of Technology Guwahati Sumanta Borah Research Scholar Dept of Mathematics Dibrugarh University Idweep Jyoti Gogoi Research Scholar Dept of Mathematics Dibrugarh University 0000-0001-5205-8915 Journal Article 2023 12 23 Let $X$ be a mixed graph and $\omega=\frac{1+\i \sqrt{3}}{2}$. We write $i\rightarrow j$, if there is an oriented edge from a vertex $v_i$ to another vertex $v_j$, and $i\sim j$ for an un-oriented edge between the vertices $v_i$ and $v_j$. The degree of a vertex $v_i$ is denoted by $d_i$. We propose the Hermitian Randi\'c matrix of second kind $R^\omega(X)\coloneqq(R^\omega_{ij})$, where $R^\omega_{ij}=\frac{1}{\sqrt{d_id_j}}$ if $i \sim j$, $R^\omega_{ij}= \frac{\omega}{\sqrt{d_id_j}}$ and $R^\omega_{ji}= \frac{\overline{\omega}}{\sqrt{d_id_j}}$ if $i\rightarrow j$, and 0 otherwise. In this paper, we investigate some spectral features of this novel Hermitian matrix and study a few properties like positiveness, bipartiteness, edge-interlacing etc. We also compute the characteristic polynomial for this new matrix and obtain some upper and lower bounds for the eigenvalues and the energy of this matrix. https://jas.shahroodut.ac.ir/article_3731_614a66ebf946b4987473e14e6558d278.pdf