The normalized distance Laplacian
نویسندگان
چکیده
Abstract The distance matrix
منابع مشابه
Eigenvalues of the normalized Laplacian
A graph can be associated with a matrix in several ways. For instance, by associating the vertices of the graph to the rows/columns and then using 1 to indicate an edge and 0 otherwise we get the adjacency matrix A. The combinatorial Laplacian matrix is defined by L = D − A where D is a diagonal matrix with diagonal entries the degrees and A is again the adjacency matrix. Both of these matrices...
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Abstract. A signed graph Γ = (G, σ) consists of an unsigned graph G = (V, E) and a mapping σ : E → {+,−}. Let Γ be a connected signed graph and L(Γ),L(Γ) be its Laplacian matrix and normalized Laplacian matrix, respectively. Suppose μ1 ≥ · · · ≥ μn−1 ≥ μn ≥ 0 and λ1 ≥ · · · ≥ λn−1 ≥ λn ≥ 0 are the Laplacian eigenvalues and the normalized Laplacian eigenvalues of Γ, respectively. In this paper, ...
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The use of spectral methods in graph theory has allowed for some amazing results where an arithmetic invariant (i.e., diameter, chromatic number, and so on) has been bounded and analyzed using analytic tools. The key has been to examine the spectrum of various matrices associated with graphs and to try to “hear the shape” of the graph from the spectrum. The three most widely used spectrums are ...
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ژورنال
عنوان ژورنال: Special Matrices
سال: 2021
ISSN: ['2300-7451']
DOI: https://doi.org/10.1515/spma-2020-0114