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Structure of the set of all minimal total dominating functions of some classes of graphs

K. Reji Kumar, Gary MacGillivray (2010)

Discussiones Mathematicae Graph Theory

In this paper we study some of the structural properties of the set of all minimal total dominating functions ( T ) of cycles and paths and introduce the idea of function reducible graphs and function separable graphs. It is proved that a function reducible graph is a function separable graph. We shall also see how the idea of function reducibility is used to study the structure of T ( G ) for some classes of graphs.

Structures ofW(2.2) Lie conformal algebra

Lamei Yuan, Henan Wu (2016)

Open Mathematics

The purpose of this paper is to study W(2, 2) Lie conformal algebra, which has a free ℂ[∂]-basis L, M such that [...] [LλL]=(∂+2λ)L,[LλM]=(∂+2λ)M,[MλM]=0 . In this paper, we study conformal derivations, central extensions and conformal modules for this Lie conformal algebra. Also, we compute the cohomology of this Lie conformal algebra with coefficients in its modules. In particular, we determine its cohomology with trivial coefficients both for the basic and reduced complexes.

Subarborians

Bohdan Zelinka (1980)

Czechoslovak Mathematical Journal

Subgraph densities in hypergraphs

Yuejian Peng (2007)

Discussiones Mathematicae Graph Theory

Let r ≥ 2 be an integer. A real number α ∈ [0,1) is a jump for r if for any ε > 0 and any integer m ≥ r, any r-uniform graph with n > n₀(ε,m) vertices and density at least α+ε contains a subgraph with m vertices and density at least α+c, where c = c(α) > 0 does not depend on ε and m. A result of Erdös, Stone and Simonovits implies that every α ∈ [0,1) is a jump for r = 2. Erdös asked whether the same is true for r ≥ 3. Frankl and Rödl gave a negative answer by showing an infinite sequence...

Sublattices of certain Coxeter lattices

Anne-Marie Bergé, Jacques Martinet (2005)

Journal de Théorie des Nombres de Bordeaux

In this paper, we describe the sublattices of some lattices, extending previous results of [Ber]. Our description makes intensive use of graphs.

Subsemi-Eulerian graphs.

Suffel, Charles, Tindell, Ralph, Hoffman, Cynthia, Mandell, Manachem (1982)

International Journal of Mathematics and Mathematical Sciences

Sufficient conditions on the existence of factors in graphs involving minimum degree

Huicai Jia, Jing Lou (2024)

Czechoslovak Mathematical Journal

For a set { A , B , C , ... } of graphs, an { A , B , C , ... } -factor of a graph G is a spanning subgraph F of G , where each component of F is contained in { A , B , C , ... } . It is very interesting to investigate the existence of factors in a graph with given minimum degree from the prospective of eigenvalues. We first propose a tight sufficient condition in terms of the Q -spectral radius for a graph involving minimum degree to contain a star factor. Moreover, we also present tight sufficient conditions based on the Q -spectral radius and the distance...

Sum labellings of cycle hypergraphs

Hanns-Martin Teichert (2000)

Discussiones Mathematicae Graph Theory

A hypergraph is a sum hypergraph iff there are a finite S ⊆ IN⁺ and d̲, [d̅] ∈ IN⁺ with 1 < d̲ ≤ [d̅] such that is isomorphic to the hypergraph d ̲ , [ d ̅ ] ( S ) = ( V , ) where V = S and = e S : d ̲ | e | [ d ̅ ] v e v S . For an arbitrary hypergraph the sum number σ = σ() is defined to be the minimum number of isolated vertices y , . . . , y σ V such that y , . . . , y σ is a sum hypergraph. Generalizing the graph Cₙ we obtain d-uniform hypergraphs where any d consecutive vertices of Cₙ form an edge. We determine sum numbers and investigate properties of sum labellings for this...

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