The complement edge metric dimension of graphs

Nirmala Mega Rosyidah, Rinurwati*

*Corresponding author for this work

Research output: Chapter in Book/Report/Conference proceedingConference contributionpeer-review

Abstract

In this paper, we construct the new concept namely the complement edge metric dimension on the graph, which is the result of combining two concepts. The first concept is edge metric dimension and in the second concept is complement metric dimension. Let given a graph G=(V(G), E(G)) where V(G) = {v1, v2, ..., vn} and also a set M = {m1, ..., mk} ⊂ V(G) that indicate connected graph and an ordered set, respectively. The representation of the edge e=xy∈E(G) with respect to M can be written as r(e|M) = (d(e, mi))=(min{d(x, mi), d(y, mi)}) where d(x, mi) and d(y, mi) indicate the distance from vertex x to mi and from vertex y to mi for i∈{1,2, ..., k}, respectively. The definition of a complement edge resolving set of G is if any two distinct edges in G have the same representation with respect to M. If set M has maximum cardinality then it is called a complement edge basis. Next, the number of vertices of M is called the complement edge metric dimension of G that can be written as edim¯(G). As a result, the complement edge metric dimension which is implemented in basic graphs, namely graph Pn, graph Sn, graph Cn, and graph Kn will be determined.

Original languageEnglish
Title of host publication7th International Conference on Mathematics - Pure, Applied and Computation
Subtitle of host publicationMathematics of Quantum Computing
EditorsMuhammad Syifa�ul Mufid, Dieky Adzkiya
PublisherAmerican Institute of Physics Inc.
ISBN (Electronic)9780735442917
DOIs
Publication statusPublished - 19 Dec 2022
Event7th International Conference on Mathematics: Pure, Applied and Computation: , ICoMPAC 2021 - Surabaya, Indonesia
Duration: 2 Oct 2021 → …

Publication series

NameAIP Conference Proceedings
Volume2641
ISSN (Print)0094-243X
ISSN (Electronic)1551-7616

Conference

Conference7th International Conference on Mathematics: Pure, Applied and Computation: , ICoMPAC 2021
Country/TerritoryIndonesia
CitySurabaya
Period2/10/21 → …

Fingerprint

Dive into the research topics of 'The complement edge metric dimension of graphs'. Together they form a unique fingerprint.

Cite this