The local multiset dimension of unicyclic graph

1st International Conference on Environmental Geography and Geography Education

生态环境科学;地球科学

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

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

Department of Mathematics Education, University of Jember, Indonesia^2

Department of Elementary School Teacher Education, University of Jember, Indonesia^3

Department of Mathematics, University of Jember, Indonesia^4

关键词: Adjacent vertices;    Cardinalities;    Graph G;    Multiset;    Ordered set;    Unicyclic graph;    Vertex set;   

Others  :  https://iopscience.iop.org/article/10.1088/1755-1315/243/1/012075/pdf
DOI  :  10.1088/1755-1315/243/1/012075

学科分类：环境科学（综合）

来源: IOP

【 摘 要 】

An unicyclic graph is a graph which contains exactly one cycle. For k-ordered set W = {s 1, s 2, , s k} of vertex set G, the multiset representation of a vertex v of G with respect to W is rm (v|W ) = {d(v, s 1), d(v, s 2), , d(v, sk )} where d(v, si ) is a distance between the vertex v and the vertices in W together with their multiplication. The resolving set W is called local resolving set of graph G if rm (v|W) ≠ rm (u|W ) for every pair u, v of adjacent vertices of G. The minimum local resolving set W is a local multiset basis of G. If G has a local multiset basis, then its cardinality is called local multiset dimension, denoted by μl (G). If G does not contain a local resolving set, then we write μl (G) = ∞. In this paper, we investigate and characterize the local multiset of some unicyclic graphs.