Proceedings of the 4th Borobudur International Symposium on Science and Technology 2022 (BIS-STE 2022)

# A Graph with Central and Local Reference Set

Authors
Yuni Listiana1, Liliek Susilowati2, *, Slamin3
1Sains and Mathematics Education Departement, Universitas Dr Soetomo, Surabaya, 60118, Indonesia
2Mathematics Departement, Universitas Airlangga, Surabaya, 60115, Indonesia
3Computer Science Departement, Universitas Jember, Jember, 68121, Indonesia
*Corresponding author. Email: liliek-s@fst.unair.ac.id
Corresponding Author
Liliek Susilowati
Available Online 9 November 2023.
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.

Open Access

Volume Title
Proceedings of the 4th Borobudur International Symposium on Science and Technology 2022 (BIS-STE 2022)
Series
Publication Date
9 November 2023
ISBN
10.2991/978-94-6463-284-2_57
ISSN
2352-5401
DOI
10.2991/978-94-6463-284-2_57How to use a DOI?
Open Access

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  -