Author:
Susilowati L,Zahidah S,Nastiti R D,Utoyo M I
Abstract
Abstract
The concept of metric dimension of graph could be applied in many graphs, one of them is subdivision graph. A subdivision graph of graph G denoted as S(G) is a graph resulting from graph G by replacing an edge uv with a new vertex w and adding two new edges uw and wv. In this paper, the subdivision graph is called k − subdivision denoted by Sk
(G), if the number of edges replaced from graph G is k for 1 ≤ k ≤ |E(G)|, where |E(G)| is the size of graph G. The purpose of this research is to find the metric dimension of subdivision graphs Sk
(G), specifically for some special graphs, those are path graph (Pn
), cycle graph (Cn
), complete graph (Kn
), star graph (Sn
), ladder graph (Ln
), book graph (Bn
), wheel graph (Wn
) and fan graph (Fn
).
Subject
General Physics and Astronomy
Reference11 articles.
1. Subdivisions of graphs: a generalization of paths and cycles;Babu;Discrete Mathematics,2008
2. Resolvability in graphs and the metric dimension of a graph;Chartrand;Discrete Appl. Math,2000
3. On the metric dimension of corona product graphs;Iswadi;Far East Journal of Mathematical Sciences,2011
4. On the fractional strong metric dimension of graphs;Kang;Discrete Applied Mathematics,2016
Cited by
3 articles.
订阅此论文施引文献
订阅此论文施引文献，注册后可以免费订阅5篇论文的施引文献，订阅后可以查看论文全部施引文献
1. On the r-dynamic chromatic number of subdivision of wheel graph;Journal of Physics: Conference Series;2022-01-01
2. On comb product graphs with respect to the complement metric dimension;INTERNATIONAL CONFERENCE ON MATHEMATICS, COMPUTATIONAL SCIENCES AND STATISTICS 2020;2021
3. The complement metric dimension of the joint graph;4TH INTERNATIONAL SCIENCES, TECHNOLOGY AND ENGINEERING CONFERENCE (ISTEC) 2020: Exploring Materials for the Future;2021