Displaying similar documents to “Green functions on self-similar graphs and bounds for the spectrum of the laplacian”

Cores and shells of graphs

Allan Bickle (2013)

Mathematica Bohemica

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The k -core of a graph G , C k ( G ) , is the maximal induced subgraph H ⊆ G such that δ ( G ) ≥ k , if it exists. For k > 0 , the k -shell of a graph G is the subgraph of G induced by the edges contained in the k -core and not contained in the ( k + 1 ) -core. The core number of a vertex is the largest value for k such that v ∈ C k ( G ) , and the maximum core number of a graph, C ^ ( G ) , is the maximum of the core numbers of the vertices of G . A graph G is k -monocore if C ^ ( G ) = δ ( G ) = k . This paper discusses some basic results on the structure of k -cores and...

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.

Equienergetic self-complementary graphs

G. Indulal, A. Vijayakumar (2008)

Czechoslovak Mathematical Journal

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In this paper equienergetic self-complementary graphs on p vertices for every p = 4 k , k ≥ 2 and p = 24 t + 1 , t ≥ 3 are constructed.

On well-covered graphs of odd girth 7 or greater

Bert Randerath, Preben Dahl Vestergaard (2002)

Discussiones Mathematicae Graph Theory

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A maximum independent set of vertices in a graph is a set of pairwise nonadjacent vertices of largest cardinality α. Plummer [14] defined a graph to be well-covered, if every independent set is contained in a maximum independent set of G. One of the most challenging problems in this area, posed in the survey of Plummer [15], is to find a good characterization of well-covered graphs of girth 4. We examine several subclasses of well-covered graphs of girth ≥ 4 with respect to the odd girth...