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On degree sets and the minimum orders in bipartite graphs

100%

Manoussakis Y., Patil H. P.

Discussiones Mathematicae Graph Theory

2014

tom 34

nr 2

383-390

For any simple graph G, let D(G) denote the degree set {degG(v) : v ∈ V (G)}. Let S be a finite, nonempty set of positive integers. In this paper, we first determine the families of graphs G which are unicyclic, bipartite satisfying D(G) = S, and further obtain the graphs of minimum orders in such families. More general, for a given pair (S, T) of finite, nonempty sets of positive integers of the same cardinality, it is shown that there exists a bipartite graph B(X, Y ) such that D(X) = S, D(Y ) = T and the minimum orders of different types are obtained for such graphs

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On cyclically embeddable graphs

80%

Woźniak M.

Discussiones Mathematicae Graph Theory

1999

tom 19

nr 2

241-248

An embedding of a simple graph G into its complement G̅ is a permutation σ on V(G) such that if an edge xy belongs to E(G), then σ(x)σ(y) does not belong to E(G). In this note we consider some families of embeddable graphs such that the corresponding permutation is cyclic.

Graphs with equal domination and 2-distance domination numbers

80%

Raczek J.

Discussiones Mathematicae Graph Theory

2011

tom 31

nr 2

375-385

Let G = (V,E) be a graph. The distance between two vertices u and v in a connected graph G is the length of the shortest (u-v) path in G. A set D ⊆ V(G) is a dominating set if every vertex of G is at distance at most 1 from an element of D. The domination number of G is the minimum cardinality of a dominating set of G. A set D ⊆ V(G) is a 2-distance dominating set if every vertex of G is at distance at most 2 from an element of D. The 2-distance domination number of G is the minimum cardinality of a 2-distance dominating set of G. We characterize all trees and all unicyclic graphs with equal domination and 2-distance domination numbers.

Ograniczanie wyników

3 Discussiones Mathematicae Graph Theory

1 Manoussakis Y.

1 Patil H. P.

1 Raczek J.

1 Woźniak M.

1 2014

1 2011

1 1999

Wyniki wyszukiwania

On degree sets and the minimum orders in bipartite graphs

On cyclically embeddable graphs

Graphs with equal domination and 2-distance domination numbers