Abstract

For a jump graph J(G) a set D ⊂ V(J(G) is a dominating set if every vertex in V(J(G))-D is adjacent to at least one vertex in D. The domination number √(J(G)) of J(G) is the minimum cardinality of a total dominating set. The non bondage number bn(J(G)) of J(G) is the maximum cardinality among all sets of edges X⊆ E(J(G)) such that √( J(G) –X) =√(J(G)). A set D⊆ V(J(G)) is a strong dominating set if every vertex in V(J(G))-D has a neighbor u in D such that the degree of u is not smaller than the degree of v, The strong domination number √s(J(G)) og J(G) is minimum cardinality of a strong dominating set. The non bondage number bsn(J(G)) of a non empty jump graph J(G) is the maximum cardinality among all sets of edges X ⊆ E(J(G)) such that √s ( J(G) –X) = √s(J(G)). In this paper some results on the non bondage number, exact values of bn(J(G)) for some standard graphs are obtained. Also some result on the strong non bondage number and bondage number are established. Also Nordhaus-Gaddum type results are found.

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References

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