On the Edge Covering Transversal Edge Domination in Graphs

E Sherin Danie, S Robinson Chellathurai

Abstract


Let G = (V,E) be any graph with nvertices and medges. An edge dominating set which intersects every minimum edge covering set in a graph Gis called an edge covering transversal edge dominating set of G. The minimum cardinality of an edge covering transversal edge dominating set is called an edge covering transversal edge domination number of Gand is denoted by \gamma_{eect}(G). Any edge covering transversal edge dominating set of cardinalities\gamma_{eect}(G) is called a \gamma_{eect}-set of G. The edge covering transversal edge domination number of some standard graphs are determined. Some properties satisfied by this concept are studied.

Keywords


Domination, dominating set, edge domination, edge covering transversal edge domination.

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References


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DOI: http://dx.doi.org/10.23755/rm.v45i0.977

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Ratio Mathematica - Journal of Mathematics, Statistics, and Applications. ISSN 1592-7415; e-ISSN 2282-8214.