Displaying similar documents to “Bounds for the (Laplacian) spectral radius of graphs with parameter α ”

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...

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.

Restrained domination in unicyclic graphs

Johannes H. Hattingh, Ernst J. Joubert, Marc Loizeaux, Andrew R. Plummer, Lucas van der Merwe (2009)

Discussiones Mathematicae Graph Theory

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Let G = (V,E) be a graph. A set S ⊆ V is a restrained dominating set if every vertex in V-S is adjacent to a vertex in S and to a vertex in V-S. The restrained domination number of G, denoted by γ r ( G ) , is the minimum cardinality of a restrained dominating set of G. A unicyclic graph is a connected graph that contains precisely one cycle. We show that if U is a unicyclic graph of order n, then γ r ( U ) ≥ ⎡ n / 3 ⎤ , and provide a characterization of graphs achieving this bound.

A note on the independent domination number of subset graph

Xue-Gang Chen, De-xiang Ma, Hua Ming Xing, Liang Sun (2005)

Czechoslovak Mathematical Journal

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The independent domination number i ( G ) (independent number β ( G ) ) is the minimum (maximum) cardinality among all maximal independent sets of G . Haviland (1995) conjectured that any connected regular graph G of order n and degree δ ≤ 1 2 n satisfies i ( G ) ≤ ⌈ 2 n 3 δ ⌉ 1 2 δ . For 1 ≤ k ≤ l ≤ m , the subset graph S m ( k , l ) is the bipartite graph whose vertices are the k - and l -subsets of an m element ground set where two vertices are adjacent if and only if one subset is contained in the other. In this paper, we give a sharp upper bound for i ( S m ( k , l ) ) and...