Displaying similar documents to “Some graphs determined by their (signless) Laplacian spectra”

Some properties of the distance Laplacian eigenvalues of a graph

Mustapha Aouchiche, Pierre Hansen (2014)

Czechoslovak Mathematical Journal

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The distance Laplacian of a connected graph G is defined by ℒ = Diag ( Tr ) - 𝒟 , where 𝒟 is the distance matrix of G , and Diag ( Tr ) is the diagonal matrix whose main entries are the vertex transmissions in G . The spectrum of ℒ is called the distance Laplacian spectrum of G . In the present paper, we investigate some particular distance Laplacian eigenvalues. Among other results, we show that the complete graph is the unique graph with only two distinct distance Laplacian eigenvalues. We establish some properties...

On the signless Laplacian spectral characterization of the line graphs of T -shape trees

Guoping Wang, Guangquan Guo, Li Min (2014)

Czechoslovak Mathematical Journal

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A graph is determined by its signless Laplacian spectrum if no other non-isomorphic graph has the same signless Laplacian spectrum (simply G is D Q S ). Let T ( a , b , c ) denote the T -shape tree obtained by identifying the end vertices of three paths P a + 2 , P b + 2 and P c + 2 . We prove that its all line graphs ℒ ( T ( a , b , c ) ) except ℒ ( T ( t , t , 2 t + 1 ) ) ( t ≥ 1 ) are D Q S , and determine the graphs which have the same signless Laplacian spectrum as ℒ ( T ( t , t , 2 t + 1 ) ) . Let μ 1 ( G ) be the maximum signless Laplacian eigenvalue of the graph G . We give the limit of μ 1 ( ℒ ( T ( a , b , c ) ) ) , too.

Bounds on Laplacian eigenvalues related to total and signed domination of graphs

Wei Shi, Liying Kang, Suichao Wu (2010)

Czechoslovak Mathematical Journal

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A total dominating set in a graph G is a subset X of V ( G ) such that each vertex of V ( G ) is adjacent to at least one vertex of X . The total domination number of G is the minimum cardinality of a total dominating set. A function f : V ( G ) → { - 1 , 1 } is a signed dominating function (SDF) if the sum of its function values over any closed neighborhood is at least one. The weight of an SDF is the sum of its function values over all vertices. The signed domination number of G is the minimum weight of an SDF on G . In...