فهرس المقالات Mardjan Hakimi-Nezhaad


  • المقاله

    1 - Normalized laplacian spectrum of two new types of join graphs
    Journal of Linear and Topological Algebra , العدد 1 , السنة 6 , زمستان 2017
    ‎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 ‎$\mathcal{D}$ ‎ أکثر
    ‎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 eigenvalues of $G$‎. ‎In this paper‎, ‎we obtain the normalized Laplacian spectrum of two new types of join graphs‎. ‎In continuing‎, ‎we determine the integrality of normalized Laplacian eigenvalues of graphs‎. ‎Finally‎, ‎the normalized Laplacian energy and degree Kirchhoff index of these new graph ‎products‎ are derived‎. تفاصيل المقالة