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...
متن کاملNormalized laplacian spectrum of two new types of join graphs
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...
متن کاملThe (normalized) Laplacian Eigenvalue of Signed Graphs
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, ...
متن کاملGeneralizing some results to the normalized Laplacian
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 ...
متن کاملAlgebraic aspects of the normalized Laplacian
Spectral graph theory looks at the interplay between the structure of a graph and the eigenvalues of a matrix associated with the graph. Many interesting graphs have rich structure which can help in determining the eigenvalues associated with some particular matrix of a graph. This survey looks at some common techniques in working with and determining the eigenvalues associated with the normali...
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ژورنال
عنوان ژورنال: Electronic Notes in Theoretical Computer Science
سال: 2019
ISSN: 1571-0661
DOI: 10.1016/j.entcs.2019.08.031