Distinguishing chromatic numbers of bipartite graphs.
Distinguishing graphs by the number of homomorphisms
A homomorphism from one graph to another is a map that sends vertices to vertices and edges to edges. We denote the number of homomorphisms from G to H by |G → H|. If 𝓕 is a collection of graphs, we say that 𝓕 distinguishes graphs G and H if there is some member X of 𝓕 such that |G → X | ≠ |H → X|. 𝓕 is a distinguishing family if it distinguishes all pairs of graphs. We show that various collections of graphs are a distinguishing family.
Distinguishing infinite graphs.
Distinguishing maps.
Distinguishing number of countable homogeneous relational structures.
Distinguishing numbers for graphs and groups.
Distributed approach for solving time-dependent problems in multimodal transport networks.
Distribution of Points of Odd Degree of Certain Triangulations in the Plane.
Domatic number and degrees of vertices of a graph
Domatic number and linear arboricity of cacti
Domatic numbers of cube graphs
Domatic numbers of lattice graphs
Domatic numbers of uniform hypergraphs
Domatically cocritical graphs
Domatically critical graphs
Dominance order and graphical partitions.
Dominant-matching graphs
We introduce a new hereditary class of graphs, the dominant-matching graphs, and we characterize it in terms of forbidden induced subgraphs.
Dominating and total dominating partitions in cubic graphs
In this paper, we continue the study of domination and total domination in cubic graphs. It is known [Henning M.A., Southey J., A note on graphs with disjoint dominating and total dominating sets, Ars Combin., 2008, 89, 159–162] that every cubic graph has a dominating set and a total dominating set which are disjoint. In this paper we show that every connected cubic graph on nvertices has a total dominating set whose complement contains a dominating set such that the cardinality of the total dominating...
Dominating bipartite subgraphs in graphs
A graph G is hereditarily dominated by a class 𝓓 of connected graphs if each connected induced subgraph of G contains a dominating induced subgraph belonging to 𝓓. In this paper we characterize graphs hereditarily dominated by classes of complete bipartite graphs, stars, connected bipartite graphs, and complete k-partite graphs.
Dominating functions of graphs with two values
The -domination number of a graph for a given number set was introduced by D. W. Bange, A. E. Barkauskas, L. H. Host and P. J. Slater as a generalization of the domination number of a graph. It is defined using the concept of a -dominating function. In this paper the particular case where for a positive integer is studied.