On the Edge Covering Transversal Edge Domination in Graphs

Authors

  • E Sherin Danie Affiliated to Manonmaniam Sundaranar University
  • S Robinson Chellathurai Affiliated to Manonmaniam Sundaranar University

DOI:

https://doi.org/10.23755/rm.v45i0.977

Keywords:

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

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.

References

Haynes T.W., Hedetniemi S.T, and Slater J.S, 1998. Fundamentals of Domination in Graphs, Marcel Decker, Inc.,

Maheswari B and Madhavi L, 2008, Vertex Domination in Mangoldt Graph, Journal of APMS, 1(2): 184 − 194.

D.B. West, Introduction to Graph Theory, Prientice-Hall of India Private Limited, New Delhi, India, 2000.

T.W. Haynes, S.T. Hedetniemi, P.J. Slater, Fundamentals of Domination in Graphs (Marcel Dekker New York,1998).

J.A. Bondy, U.S.R. Murty, Graph Theory with application, Elsevier Science Publishing Co, Sixth Printing, 1984.

Ismail Sahul Hamid, Independent transversal Domination in Graphs, Discussiones Mathematicae, Graph Theory 32(2012)5 − 17.

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Published

2023-01-30

Issue

Vol. 45 (2023): Special Issue: Advances in Applied and Intellectual Mathematics

Section

Volume 44-2022

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