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Publication Details
AFRICAN RESEARCH NEXUS
SHINING A SPOTLIGHT ON AFRICAN RESEARCH
mathematics
Strong equality of domination parameters in trees
Discrete Mathematics, Volume 260, No. 1-3, Year 2003
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Description
We study the concept of strong equality of domination parameters. Let P1 and P2 be properties of vertex subsets of a graph, and assume that every subset of V(G) with property P2 also has property P1. Let ψ1(G) and ψ2(G), respectively, denote the minimum cardinalities of sets with properties P1 and P2, respectively. Then ψ1(G) ≤ ψ2(G). If ψ1(G)=ψ2(G) and every ψ1(G)-set is also a ψ2(G)-set, then we say ψ1(G) strongly equals ψ2(G), written ψ1(G) = ψ2(G). We provide a constructive characterization of the trees T such that γ(T) = i(T), where γ(T) and i(T) are the domination and independent domination numbers, respectively. A constructive characterization of the trees T for which γ(T) = γt(T), where γt(T) denotes the total domination number of T, is also presented. © 2002 Elsevier Science B.V. All rights reserved.
Authors & Co-Authors
Haynes, Teresa W.
United States, Johnson
East Tennessee State University
Henning, Michael A.
South Africa, Durban
University of Kwazulu-natal
Slater, Peter J.
United States, Huntsville
The University of Alabama in Huntsville
Statistics
Citations: 28
Authors: 3
Affiliations: 3
Identifiers
Doi:
10.1016/s0012-365x(02)00451-x
ISSN:
0012365X