Super domination number of unicyclic graphs
Ridho Alfarisi, Dafik Dafik, Robiatul Adawiyah, Rafiantika Megahnia Prihandini, Ermita Rizki Albirri, Ika Hesti Agustin · IOP Conference Series Earth and Environmental Science · 2019
All graphs in this paper are a connected graph, denoted by G = ( V, E ).The open neighbourhood of a vertex v of a graph G is the set N ( v ) consisting of all vertices adjacent to v in G . For D ⊂ V ( G ), we define D = V ( G )\ D , a set D ⊂ V ( G ) is called a dominating set of G if for every vertex in D has at least one neighbour in D , N ( v ) ∩ D ≠ for every u ∈ D The minimum cardinality of all dominating set in G , is the domination number, denoted by γ( G ). A set D ⊂ V ( G ) is called a super dominating set of G if for every vertex u ∈ D , there is exists v ∈ D such that N ( v ) ∩ D = { u }. The super domination number of G is the minimum cardinality among all super dominating sets in G , denoted by γ sp ( G ). In this paper, we investigate the super domination number of unicyclic graphs namely ( m, n )-tadpole graph, n –pan graph, sun graphs, cycle with two neighbour pendant vertex, and cartepillar with adding one edge.