Super domination number of unicyclic graphs

1st International Conference on Environmental Geography and Geography Education

生态环境科学;地球科学

Alfarisi, R.^1^2 ; Dafik^1^3 ; Adawiyah, R.^1^3 ; Prihandini, R.M.^1^2 ; Albirri, E.R.^1^3 ; Agustin, I.H.^1^4

CGANT-Research Group, University of Jember, Indonesia^1

Department of Elementary School Teacher Education, University of Jember, Indonesia^2

Department of Mathematics Education, University of Jember, Indonesia^3

Department of Mathematics, University of Jember, Indonesia^4

关键词: Cardinalities;    Connected graph;    Dominating sets;    Domination number;    Graph G;    Neighbourhood;    Pendant vertices;    Unicyclic graph;   

Others  :  https://iopscience.iop.org/article/10.1088/1755-1315/243/1/012074/pdf
DOI  :  10.1088/1755-1315/243/1/012074

学科分类：环境科学（综合）

来源: IOP

【 摘 要 】

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 γsp(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.