Digraphs maximal with respect to connectivity
Dimension of the sum of two copies of a graph
Directed graphs and matrix equations
Disjoint Edges in Geometric Graphs.
Distance in graphs
Distance-Locally Disconnected Graphs
For an integer k ≥ 1, we say that a (finite simple undirected) graph G is k-distance-locally disconnected, or simply k-locally disconnected if, for any x ∈ V (G), the set of vertices at distance at least 1 and at most k from x induces in G a disconnected graph. In this paper we study the asymptotic behavior of the number of edges of a k-locally disconnected graph on n vertices. For general graphs, we show that this number is Θ(n2) for any fixed value of k and, in the special case of regular graphs,...
Distances between rooted trees
Two types of a distance between isomorphism classes of graphs are adapted for rooted trees.
Domatic number and degrees of vertices of a graph
Domatic numbers of lattice graphs
Domatically critical graphs
Domination and leaf density in graphs
The domination number γ(G) of a graph G is the minimum cardinality of a subset D of V(G) with the property that each vertex of V(G)-D is adjacent to at least one vertex of D. For a graph G with n vertices we define ε(G) to be the number of leaves in G minus the number of stems in G, and we define the leaf density ζ(G) to equal ε(G)/n. We prove that for any graph G with no isolated vertex, γ(G) ≤ n(1- ζ(G))/2 and we characterize the extremal graphs for this bound. Similar results are obtained for...
Domination in graphs with few edges
The domination number of a graph and two its variants are considered, namely the signed domination number and the minus domination number . These numerical invariants are compared for graphs in which the degrees of vertices do not exceed 3.
Domination in Kneser graphs
The domination number and the domatic number of a certain special type of Kneser graphs are determined.
Domination, independence and irredundance in graphs [Book]
Dual point-partition number of complementary graphs
Dynamic cage survey.
Ecken mit starken Zusammenhangseigenschaften in endlichen Graphen.
Edge Bases of Complete Uniform Hypergraphs
Edge domination in graphs of cubes
The signed edge domination number and the signed total edge domination number of a graph are considered; they are variants of the domination number and the total domination number. Some upper bounds for them are found in the case of the -dimensional cube .
Edge maximal -edge disjoint free graphs
For two positive integers r and s, 𝓖(n;r,s) denotes to the class of graphs on n vertices containing no r of s-edge disjoint cycles and f(n;r,s) = max{𝓔(G):G ∈ 𝓖(n;r,s)}. In this paper, for integers r ≥ 2 and k ≥ 1, we determine f(n;r,2k+1) and characterize the edge maximal members in 𝓖(n;r,2k+1).