Randi´c Matrix and Randi´c Energy of Uniform Hypergraphs

Abstract

‎The Randi´c matrix $R=[r_{ij}]$ of a graph $ G=(V,E) $ was defined as $r_{ij}=\frac{1}{\sqrt{d_id_j}}$ if vertices $v_i$ and $v_j$ are adjacent and $r_{ij}=0$ otherwise‎, ‎where $d_i$ is the degree of the vertex $v_i\in V$‎. ‎In this paper‎, ‎we define the Randi´c matrix of a uniform hypergraph and study some its spectral properties‎. ‎We also define the Randi´c energy of a uniform hypergraph and determine some upper and lower bound for it‎.

Keywords

• randi´c matrix‎
• ‎randi´c energy‎
• ‎uniform hypergraph‎
• ‎eigenvalue‎