The Laplacian spectrum of corona of two graphs
نویسندگان
چکیده
منابع مشابه
The Laplacian Spectrum of Corona of Two Graphs
Let G1,G2 be two connected graphs. Denote the corona and the edge corona of G1, G2 by G1 ◦ G2 and G = G1 G2, respectively. In this paper, we compute the Laplacian spectrum of the corona G◦H of two arbitrary graphs G and H and the edge corona of a connected regular graph G1 and an arbitrary graph G2.
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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 ...
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Abstract. Given two graphs G1, with vertices 1, 2, ..., n and edges e1, e2, ..., em, and G2, the edge corona G1 ⋄G2 of G1 and G2 is defined as the graph obtained by taking m copies of G2 and for each edge ek = ij of G, joining edges between the two end-vertices i, j of ek and each vertex of the k-copy of G2. In this paper, the adjacency spectrum and Laplacian spectrum of G1 ⋄ G2 are given in te...
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The paper is essentially a survey of known results about the spectrum of the Laplacian matrix of graphs with special emphasis on the second smallest Laplacian eigenvalue λ2 and its relation to numerous graph invariants, including connectivity, expanding properties, isoperimetric number, maximum cut, independence number, genus, diameter, mean distance, and bandwidth-type parameters of a graph. S...
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ژورنال
عنوان ژورنال: Kragujevac Journal of Mathematics
سال: 2014
ISSN: 1450-9628
DOI: 10.5937/kgjmath1401163l