Cototal edge domination number of a graph

S.B. Anupama; Y. B. Maralabhavi; Venkanagouda M. Goudar

doi:10.26637/mjm402/017

Abstract

A set $F$ of a graph $G(V, E)$ is an edge dominating set if every edge in $E-F$ is adjacent to some edge in $F$ . An edge domination number $\gamma^{\prime}(G)$ of $G$ is the minimum cardinality of an edge dominating set. An edge dominating set $F$ is called a cototal edge dominating set if the induced subgraph $\langle E-F\rangle$ doesnot contain isolated edge. The minimum cardinality of the cototal edge dominating set in $G$ is its domination number and is denoted by $\gamma_{c o t}^{\prime}(G)$ . We investigate several properties of cototal edge dominating sets and give some bounds on the cototal edge domination number.

Keywords:

Edge domination number, cototal edge domination number

Mathematics Subject Classification:

05C78

Authors Imprint References Funding Related Articles Downloads

S.B. Anupama Research Scholar, Department of Mathematics, Bangalore University, Bengaluru- 560001, Karnataka, India.
Y. B. Maralabhavi Department of Mathematics, Bangalore University, Bengaluru- 560001, Karnataka, India.
Venkanagouda M. Goudar Department of Mathematics, Sri Siddhartha Institute of Technology, Tumkur -572105, Karnataka, India https://orcid.org/0000-0002-9738-4236

Pages: 325-337
Date Published: 01-04-2016
Vol. 4 No. 02 (2016): Malaya Journal of Matematik (MJM)

R.B. Allan and R. Laskar, On domination and independent domination numbers of a graph, Discrete Math, 23(1978), 73-76. DOI: https://doi.org/10.1016/0012-365X(78)90105-X

S. Arumugam and S. Velammal, Edge domination in graphs, Taiwaness Journal of Mathematics, 2(1998), 173-179. DOI: https://doi.org/10.11650/twjm/1500406930

Doost Ali Mojdeh and Razieh Sadeghi, Independendent edge dominating set of certain graphs, International Mathematical Forum, 2(7)(2007), 315-320. DOI: https://doi.org/10.12988/imf.2007.07029

F. Harary, Graph theory, Addison-Wesley, Reading Mass (1969). DOI: https://doi.org/10.21236/AD0705364

T. W. Haynes, S. T. Hedetniemi and P. J. Slater, Fundamentals of domination in graphs, Marcel Dekker, Inc., New York, (1998).

V.R.Kulli, B.Janakiram and R.R.Iyer, The cototal domination number of a graph, J. Discrete Mathematical Sciences and Cryptography 2(1999), 179-184. DOI: https://doi.org/10.1080/09720529.1999.10697889

S.Mitchell and S.T. Hedetniemi, Edge domination in trees, Congr. Numer., 19(1977), 489-509.