Notes on domination in fuzzy graphs

Article type: Research Article

Authors: Manjusha, O.T. | Sunitha, M.S.

Affiliations: Department of Mathematics, Kerala Govt. Polytechnic College, Westhill, Kozhikode, India | Department of Mathematics, National Institute of Technology, Calicut, India

Note: [] Corresponding author. O.T. Manjusha, Department of Mathematics, Kerala Govt. Polytechnic College, Westhill, Kozhikode 673005, India. Emails: [email protected] (O.T. Manjusha), [email protected] (M.S. Sunitha).

Abstract: In this paper different types of degrees of a node in fuzzy graphs are discussed. The domination number of $K_{\sigma_{1},\sigma_{2}}$ as given in the paper “Domination in fuzzy graphs-I” by A. Somasundaram and S. Somasundaram is modified. A lower bound and an upper bound for the domination number of fuzzy graphs are obtained. Domination in fuzzy trees is studied. It is established that the set of fuzzy cut nodes of a fuzzy tree is a dominating set and obtained a necessary and sufficient condition for the set of fuzzy end nodes to be a dominating set. Also it is proved that in a fuzzy tree each node of a dominating set is incident on a fuzzy bridge.

Keywords: Fuzzy graph, strong arcs, domination number

DOI: 10.3233/IFS-141277

Journal: Journal of Intelligent & Fuzzy Systems, vol. 27, no. 6, pp. 3205-3212, 2014