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- W4360593863 abstract "The normalized distance Laplacian matrix of a connected graph $ G $, denoted by $ D^{mathcal{L}}(G) $, is defined by $ D^{mathcal{L}}(G)=Tr(G)^{-1/2}D^L(G)Tr(G)^{-1/2}, $ where $ D(G) $ is the distance matrix, the $D^{L}(G)$ is the distance Laplacian matrix and $ Tr(G)$ is the diagonal matrix of vertex transmissions of $ G. $ The set of all eigenvalues of $ D^{mathcal{L}}(G) $ including their multiplicities is the normalized distance Laplacian spectrum or $ D^{mathcal{L}} $-spectrum of $G$. In this paper, we find the $ D^{mathcal{L}} $-spectrum of the joined union of regular graphs in terms of the adjacency spectrum and the spectrum of an auxiliary matrix. As applications, we determine the $ D^{mathcal{L}} $-spectrum of the graphs associated with algebraic structures. In particular, we find the $ D^{mathcal{L}} $-spectrum of the power graphs of groups, the $ D^{mathcal{L}} $-spectrum of the commuting graphs of non-abelian groups and the $ D^{mathcal{L}} $-spectrum of the zero-divisor graphs of commutative rings. Several open problems are given for further work." @default.
- W4360593863 created "2023-03-24" @default.
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- W4360593863 date "2022-07-30" @default.
- W4360593863 modified "2023-09-29" @default.
- W4360593863 title "On normalized distance Laplacian eigenvalues of graphs and applications to graphs defined on groups and rings" @default.
- W4360593863 doi "https://doi.org/10.37193/cjm.2023.01.14" @default.
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