Split Edge Geodetic Domination Number of a Graph. Issue 1 (June 2021) - Arul Paul Sudhahar, P.; Jeba Lisa, J.
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 .