On the k-Metric Dimension of a Barbell Graph and a t-fold Wheel Graph

DOI

10.2991/assehr.k.200827.111How to use a DOI?

Keywords

k-metric dimension, k-metric generator, barbell graph, t-fold wheel graph

Abstract

Let G be a connected and simple graph with the vertex set V(G) and the edge set E(G). The set S ⊆ V (G) is called a k-metric generator for G if and only if for every two pairs different vertices u,v ∈ V(G), there are at least k vertices w1,w2,..,wk ∈ S such that d(u,wi) ≠ d(v,wi) for every i ∈ {1, 2, …, k}, with d(u,v) is the length of shortest u – v path. A minimum k-metric generator is called a k-metric basis and its cardinality is called the k-metric dimension of G, denoted by dimk(G). A barbell graph Bn,n for n ≥ 3 is the simple graph obtained from two complete graph Kn connected by a bridge. A t-fold wheel graph Wnt for t ≥ 2 and n ≥ 3 is the simple graph that contain the central t vertex which are adjacent to each vertex in a cycle, but not adjacent to each other. In this paper, we determine the k-metric dimension of a barbell graph and a t-fold wheel graph.

Copyright

© 2020, the Authors. Published by Atlantis Press.

Open Access

This is an open access article distributed under the CC BY-NC license (http://creativecommons.org/licenses/by-nc/4.0/).

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TY  - CONF
AU  - Eri Setyawan
AU  - Tri Atmojo Kusmayadi
PY  - 2020
DA  - 2020/08/28
TI  - On the k-Metric Dimension of a Barbell Graph and a t-fold Wheel Graph
BT  - Proceedings of the SEMANTIK Conference of Mathematics Education (SEMANTIK 2019)
PB  - Atlantis Press
SP  - 23
EP  - 26
SN  - 2352-5398
UR  - https://doi.org/10.2991/assehr.k.200827.111
DO  - 10.2991/assehr.k.200827.111
ID  - Setyawan2020
ER  -