Domination and leaf density in graphs

• Autorzy: Anders Sune Pedersen
• Języki publikacji: EN

Abstrakty

EN

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 the total domination number and the partition domination number.

Słowa kluczowe

EN

bounds; domination number; leaves; partioned domination; total domination number

Kategorie tematyczne

• 05C35: Extremal problems
• 05C75: Structural characterization of families of graphs
• 05C69: Dominating sets, independent sets, cliques

• Wydawca: De Gruyter Open
• Czasopismo: Discussiones Mathematicae Graph Theory
• Rocznik: 2005
• Tom: 25
• Numer: 3
• Strony: 251-259

Daty

wydano

2005

otrzymano

2003-05-19

poprawiono

2003-10-01

Twórcy

autor

Anders Sune Pedersen

• Department of Mathematics, Aalborg University, Fredrik Bajers Vej 7G, DK 9220 Aalborg, Denmark

Bibliografia

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Identyfikatory

DOI

10.7151/dmgt.1278