Regarding Edge Domination in Hypergraph

D. K. Thakkar; V. R. Dave

doi:https://doi.org/10.14445/22315373/IJMTT-V44P521

International Journal of Mathematics Trends and Technology

Research Article | Open Access | Download PDF

Volume 44 | Number 3 | Year 2017 | Article Id. IJMTT-V44P521 | DOI : https://doi.org/10.14445/22315373/IJMTT-V44P521

Regarding Edge Domination in Hypergraph

D. K. Thakkar, V. R. Dave

Citation :

D. K. Thakkar, V. R. Dave, "Regarding Edge Domination in Hypergraph," International Journal of Mathematics Trends and Technology (IJMTT), vol. 44, no. 3, pp. 108-114, 2017. Crossref, https://doi.org/10.14445/22315373/IJMTT-V44P521

Abstract

In this paper we further prove more results about edge domination in hypergraphs. In particular we prove necessary & sufficient conditions under which the edge domination number of a hypergraph increases or decreases when an edge is added or removed from the hypergraph. We have proved thatif E(G – v) >E(G) & if F is a minimum edge dominating set of G then there is an edge e containing v  e  F &Prn[e, F] contains two distinct edges also we have proved that if E(G + h) <E(G) then there are at least two vertices x & y in h  all the edges containing x or y except h are in the complement of F. Where F is any minimum edge dominating set of G + h.

Keywords

Hypergraph, Dominating Set in Hypergraph,Edge Dominating Set, Edge Domination Number, Minimal Edge Dominating Set, Minimum Edge Dominating Set, Edge Degree, Edge Neighbourhood, Sub Hypergraph, Partial Sub Hypergraph, Dual Hypergraph, edge addition, edge removal. AMS Subject Classification (2010): 05C15, 05C69, 05C65

References

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