On the local adjacency metric dimension of split graph

1st International Conference on Environmental Geography and Geography Education

生态环境科学;地球科学

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

CGANT-University of Jember, Jember, Indonesia^1

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

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

Department of Elementary School Education, University of Jember, Jember, Indonesia^4

关键词: Cardinalities;    Finite graphs;    Graph G;    Metric dimensions;    Order sets;    Split graphs;   

Others  :  https://iopscience.iop.org/article/10.1088/1755-1315/243/1/012076/pdf
DOI  :  10.1088/1755-1315/243/1/012076

学科分类：环境科学（综合）

来源: IOP

【 摘 要 】

The metric dimension is one of an interesting studied graph topics. The local adjacency metric dimension is combination of the local metric dimension and the adjacency metric dimension. The graph G = (V, E) in this study is connected, simple, and finite graph. Let u, v are in G. For an order set of vertices X = {x 1, x 2, , xk }, the adjacency representation of v with respect to X is the ordered k-tuple rA(v|X) = (dA(v, x 1), dA(v, x 2), , dA(v, xk )), where dA(u, v) represents the adjacency distance u - v. dA(u, v) is defined by 0 if u = vi , 1 if u adjacents with v, and 2 if u does not adjacent with v. For every two distinct vertices u, v and u adjacents with v such that rA(u|X) ≠ rA(v|X). Then, we call X as local adjacency resolving set of G. The basis of G is a minimum local adjacency resolving set in G. The vertex cardinality in the basis is a local adjacency metric dimension of G (dimA, l (G)). In this research, we initiate to study the existence of the local adjacency metric dimension of split graph G.