Upper eccentric domination in graphs. (4th July 2019)

• Record Type: Journal Article
• Authors: Bhanumathi, M.; Abirami, R. Meenal
• Is Part Of: Journal of discrete mathematical sciences & cryptography. Volume 22:Number 5(2019)
• Page Start: 835
• Page End: 846
• Publication Date: 2019-07-04
• Subjects: 05C12 -- 05C69; Domination -- Eccentric domination -- Upper Eccentric Domination; Computer science -- Mathematics -- Periodicals; Cryptography -- Periodicals; Computer science -- Mathematics; Cryptography; Periodicals; 004.0151
• DOI: 10.1080/09720529.2019.1685236
• Languages: English
• ISSNs: 0972-0529

Abstract

Abstract: A set S ⊆ V is said to be a dominating set in a graph G if every vertex in V – S is adjacent to some vertex in S and the domination number of G is defined to be the minimum cardinality of a dominating set in G . A dominating set D is said to be an eccentric dominating set if for every v ∈ V–D, there exists at least one eccentric vertex of v in D . An eccentric dominating set D is a minimal eccentric dominating set if no proper subset S ⊂ D is an eccentric dominating set. In this paper, we introduce a new parameter known as upper eccentric domination number. The upper eccentric domination number ⎾ ed ( G ) of a graph G equals the maximum cardinality of a minimal eccentric dominating set, that is ⎾ ed ( G ) = max | D |, where the maximum is taken over D in D ', where D ' is the set of all minimal eccentric dominating sets of G .