‎Let $G$ be a graph of order $n$ with vertices labeled as $v_1‎, ‎v_2,dots‎ , ‎v_n$‎. ‎Let $d_i$ be the degree of the vertex $v_i$ for $i = 1‎, ‎2‎, ‎cdots‎ , ‎n$‎. ‎The Albertson matrix of $G$ is the square matrix of order $n$ whose $(i‎, ‎j)$-entry is equal to $|d_i‎ - ‎d_j|$ if $v_i $ is adjacent to $v_j$ and zero‎, ‎otherwise‎. ‎The main purposes of this paper is to introduce the Albertson ...

‎Let $G$ be a graph without an isolated vertex‎, ‎the normalized Laplacian matrix $tilde{mathcal{L}}(G)$‎ ‎is defined as $tilde{mathcal{L}}(G)=mathcal{D}^{-frac{1}{2}}mathcal{L}(G)mathcal{D}^{-frac{1}{2}}$‎, where ‎$mathcal{D}$ ‎is a‎ diagonal matrix whose entries are degree of ‎vertices ‎‎of ‎$‎G‎$‎‎. ‎The eigenvalues of‎ $tilde{mathcal{L}}(G)$ are ‎called as ‎the ‎normalized Laplacian eigenva...