Asymptotic Behaviour of Cuboids Optimising Laplacian Eigenvalues
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DOI: 10.1007/s00020-017-2407-5
Abstract: We prove that in dimension $$n \ge 2$$n≥2, within the collection of unit-measure cuboids in $$\mathbb {R}^n$$Rn (i.e. domains of the form $$\prod _{i=1}^{n}(0, a_n)$$∏i=1n(0,an)), any sequence of minimising domains $$R_k^\mathcal {D}$$RkD for the Dirichlet… read more here.
Keywords: cuboids optimising; asymptotic behaviour; rightarrow infty; laplacian eigenvalues ... See more keywords
Multiplicities of distance Laplacian eigenvalues and forbidden subgraphs
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DOI: 10.1016/j.laa.2017.11.031
Abstract: Abstract In this work, the graphs of order n having the second distance Laplacian eigenvalue of multiplicity n − 2 are determined. Besides that, this result also characterizes the graphs where the multiplicity of some… read more here.
Keywords: multiplicity; multiplicities distance; laplacian eigenvalues; distance laplacian ... See more keywords
Improved results on Brouwer's conjecture for sum of the Laplacian eigenvalues of a graph
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DOI: 10.1016/j.laa.2018.08.003
Abstract: Abstract Let G be a graph with n vertices and m edges, and let S k ( G ) be the sum of the k largest Laplacian eigenvalues of G. It was conjectured by Brouwer… read more here.
Keywords: conjecture sum; laplacian eigenvalues; improved results; brouwer conjecture ... See more keywords
Graphs whose Laplacian eigenvalues are almost all 1 or 2
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DOI: 10.1515/spma-2024-0015
Abstract: Abstract We explicitly determine all connected graphs whose Laplacian matrices have at most four eigenvalues different from 1 and 2. read more here.
Keywords: graphs whose; whose laplacian; eigenvalues almost; laplacian eigenvalues ... See more keywords
On the Sum and Spread of Reciprocal Distance Laplacian Eigenvalues of Graphs in Terms of Harary Index
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DOI: 10.3390/sym14091937
Abstract: The reciprocal distance Laplacian matrix of a connected graph G is defined as RDL(G)=RT(G)−RD(G), where RT(G) is the diagonal matrix of reciprocal distance degrees and RD(G) is the Harary matrix. Clearly, RDL(G) is a real… read more here.
Keywords: rdl rdl; distance laplacian; distance; laplacian eigenvalues ... See more keywords