Split Edge Geodetic Domination Number of a Graph. Issue 1 (June 2021)

• Record Type: Journal Article
• Authors: Arul Paul Sudhahar, P.; Jeba Lisa, J.
• Is Part Of: Journal of physics. Volume 1947:Issue 1(2021)
• Publication Date: 2021-06
• Subjects: edge geodetic number -- domination number -- edge geodetic domination number -- split edge geodetic domination number; 05C12; Physics -- Congresses; 530.5
• DOI: 10.1088/1742-6596/1947/1/012022
• Languages: English
• ISSNs: 1742-6588

Abstract

Abstract: In this paper, we introduce a new graph theoretic parameter, split edge geodetic domination number of a connected graph as follows. A set S ⊆ V ( G ) is said to be a split edge geodetic dominating set of G if S is both a split edge geodetic set and a dominating set of G ( < V - S > is disconnected). The minimum cardinality of the split edge geodetic dominating set of G is called split edge geodetic domination number of G and is denoted by γ 1 g s ( G ). It is shown that for any 3 positive integers m, f and n with 2 ≤ m ≤ f ≤ n -2, there exists a connected graph G of order n such that g 1 ( G ) = m and γ 1 g s ( G ) = f . For every pair l, n of integers with 2 ≤ l ≤ n -2, there exists a connected graph G of order n such that γ 1 g s ( G ) = l .