A Graph with Central and Local Reference Set

DOI

10.2991/978-94-6463-284-2_57How to use a DOI?

Keywords

Local metric; Graph; New development

Abstract

The local metric set is a subset of vertex set in graph that introduced by Okamoto et al. It is referred to a subset where is for every two adjacent vertices in graph has different representation with the subset. Previously, Slater introduced the location set and reference set as another term of resolving set and minimum resolving set, respectively. In this paper, we are developing a new concept refer to locating set and reference set by Slater and local metric set by Okamoto, then combaining it with a central vertices of a simple and connected graph called as central local metric set and central local reference set. We are developed the new concept by observation and literature study of related concept. We used some class of graph, such as complete graph ( K n ) , complete bipartite graph ( K n , m ) , and sun graph ( S n ) to apply main definition of central local metric set and find their central local reference set. Then, the result will be formulated in a theorema that apply for general case. The result of this paper show that the central local reference set of K n and K n , m are equal with their vertex set. Meanwhile, the central local reference set of sun graph is equal with vertex set of its cycle. This is given a implication that since both of radius and diameter of K n and K n , m are equal so their central local metric dimension equal with their total vertex, meanwhile on sun graph both of radius and diameter different.

Copyright

© 2023 The Author(s)

Open Access

Open Access This chapter is licensed under the terms of the Creative Commons Attribution-NonCommercial 4.0 International License (http://creativecommons.org/licenses/by-nc/4.0/), which permits any noncommercial use, sharing, adaptation, distribution and reproduction in any medium or format, as long as you give appropriate credit to the original author(s) and the source, provide a link to the Creative Commons license and indicate if changes were made.

Download article (PDF)

TY  - CONF
AU  - Yuni Listiana
AU  - Liliek Susilowati
AU  - Slamin
PY  - 2023
DA  - 2023/11/09
TI  - A Graph with Central and Local Reference Set
BT  - Proceedings of the 4th Borobudur International Symposium on Science and Technology 2022 (BIS-STE 2022)
PB  - Atlantis Press
SP  - 515
EP  - 524
SN  - 2352-5401
UR  - https://doi.org/10.2991/978-94-6463-284-2_57
DO  - 10.2991/978-94-6463-284-2_57
ID  - Listiana2023
ER  -