All a b c d e f g h i j k l m n o p q r s t u v w x y z Other

Previous Page 8 Next

Displaying 141 – 160 of 227

Showing per page

Nordhaus-Gaddum-Type Results for Resistance Distance-Based Graph Invariants

Kinkar Ch. Das, Yujun Yang, Kexiang Xu (2016)

Discussiones Mathematicae Graph Theory

Two decades ago, resistance distance was introduced to characterize “chemical distance” in (molecular) graphs. In this paper, we consider three resistance distance-based graph invariants, namely, the Kirchhoff index, the additive degree-Kirchhoff index, and the multiplicative degree-Kirchhoff index. Some Nordhaus-Gaddum-type results for these three molecular structure descriptors are obtained. In addition, a relation between these Kirchhoffian indices is established.

Note on a conjecture for the sum of signless Laplacian eigenvalues

Xiaodan Chen, Guoliang Hao, Dequan Jin, Jingjian Li (2018)

Czechoslovak Mathematical Journal

For a simple graph G on n vertices and an integer k with 1 ≤ k ≤ n , denote by 𝒮 k + ( G ) the sum of k largest signless Laplacian eigenvalues of G . It was conjectured that 𝒮 k + ( G ) ≤ e ( G ) + k + 1 2 , where e ( G ) is the number of edges of G . This conjecture has been proved to be true for all graphs when k ∈ { 1 , 2 , n - 1 , n } , and for trees, unicyclic graphs, bicyclic graphs and regular graphs (for all k ). In this note, this conjecture is proved to be true for all graphs when k = n - 2 , and for some new classes of graphs.

Note on a Lovász's result

Dănuţ Marcu (1997)

Mathematica Bohemica

In this paper, we give a generalization of a result of Lovasz from [2].

Note on cyclic decompositions of complete bipartite graphs into cubes

Dalibor Fronček (1999)

Discussiones Mathematicae Graph Theory

So far, the smallest complete bipartite graph which was known to have a cyclic decomposition into cubes Q d of a given dimension d was K d 2 d - 1 , d 2 d - 2 . We improve this result and show that also K d 2 d - 2 , d 2 d - 2 allows a cyclic decomposition into Q d . We also present a cyclic factorization of K 8 , 8 into Q₄.

Note on enumeration of labeled split graphs

Vladislav Bína, Jiří Přibil (2015)

Commentationes Mathematicae Universitatis Carolinae

The paper brings explicit formula for enumeration of vertex-labeled split graphs with given number of vertices. The authors derive this formula combinatorially using an auxiliary assertion concerning number of split graphs with given clique number. In conclusion authors discuss enumeration of vertex-labeled bipartite graphs, i.e., a graphical class defined in a similar manner to the class of split graphs.

Note on graphs colouring

Dănuţ Marcu (1992)

Mathematica Bohemica

In this paper, we show that the maximal number of minimal colourings of a graph with n vertices and the chromatic number k is equal to k n - k , and the single graph for which this bound is attained consists of a k -clique and n - k isolated vertices.

Note on group distance magic complete bipartite graphs

Sylwia Cichacz (2014)

Open Mathematics

A Γ-distance magic labeling of a graph G = (V, E) with |V| = n is a bijection ℓ from V to an Abelian group Γ of order n such that the weight w ( x ) = ∑ y ∈ N G ( x ) ℓ ( y ) of every vertex x ∈ V is equal to the same element µ ∈ Γ, called the magic constant. A graph G is called a group distance magic graph if there exists a Γ-distance magic labeling for every Abelian group Γ of order |V(G)|. In this paper we give necessary and sufficient conditions for complete k-partite graphs of odd order p to be ℤp-distance magic. Moreover...

Currently displaying 141 – 160 of 227