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Distance-Locally Disconnected Graphs

Mirka Miller, Joe Ryan, Zdeněk Ryjáček (2013)

Discussiones Mathematicae Graph Theory

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

Bohdan Zelinka (1991)

Mathematica Bohemica

Two types of a distance between isomorphism classes of graphs are adapted for rooted trees.

Domination and leaf density in graphs

Anders Sune Pedersen (2005)

Discussiones Mathematicae Graph Theory

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

Bohdan Zelinka (1995)

Mathematica Bohemica

The domination number ( G ) of a graph G and two its variants are considered, namely the signed domination number s ( G ) and the minus domination number - ( G ) . These numerical invariants are compared for graphs in which the degrees of vertices do not exceed 3.

Domination in Kneser graphs

Jaroslav Ivančo, Bohdan Zelinka (1993)

Mathematica Bohemica

The domination number and the domatic number of a certain special type of Kneser graphs are determined.

Dynamic cage survey.

Exoo, Geoffrey, Jajcay, Robert (2008)

The Electronic Journal of Combinatorics [electronic only]

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