On (local) metric dimension of graphs with m-pendant points

International Conference on Mathematics: Education, Theory and Application

数学;教育

Rinurwati^1,2 ; Slamin^3 ; Suprajitno, H.^1

Mathematics Department, Universitas Airlangga, Indonesia^1

Mathematics Department, Sepuluh Nopember Institute of Technology, Indonesia^2

Information System of Study Program, Universitas Jember, Indonesia^3

关键词: Adjacent vertices;    Cardinalities;    Connected graph;    Metric dimensions;    Ordered set;    Two-graphs;    Upper Bound;   

Others  :  https://iopscience.iop.org/article/10.1088/1742-6596/855/1/012035/pdf
DOI  :  10.1088/1742-6596/855/1/012035

学科分类：发展心理学和教育心理学

来源: IOP

【 摘 要 】

An ordered set of vertices S is called as a (local) resolving set of a connected graph G = (VG, EG) if for any two adjacent vertices s ≠ t ∈ VGhave distinct representation with respect to S, that is r(s | S) ≠ r(t | S). A representation of a vertex in G is a vector of distances to vertices in S. The minimum (local) resolving set for G is called as a (local) basis of G. A (local) metric dimension for G denoted by dim(G), is the cardinality of vertices in a basis for G, and its local variant by diml(G). Given two graphs, G with vertices s1, s2, , spand edges e1, e2, , eq, and H. An edge-corona of G and H, GH is defined as a graph obtained by taking a copy of G and q copies of H and for each edge ej= sishof G joining edges between the two end-vertices si, shof ejand each vertex of j-copy of H. In this paper, we determine and compare between the metric dimension of graphs with m-pendant points, GmK1, and its local variant for any connected graph G. We give an upper bound of the dimensions.