# 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 language English 7th International Conference on Mathematics - Pure, Applied and Computation Mathematics of Quantum Computing Muhammad Syifa�ul Mufid, Dieky Adzkiya American Institute of Physics Inc. 9780735442917 https://doi.org/10.1063/5.0131823 Published - 19 Dec 2022 7th International Conference on Mathematics: Pure, Applied and Computation: , ICoMPAC 2021 - Surabaya, IndonesiaDuration: 2 Oct 2021 → …

### Publication series

Name AIP Conference Proceedings 2641 0094-243X 1551-7616

### Conference

Conference 7th International Conference on Mathematics: Pure, Applied and Computation: , ICoMPAC 2021 Indonesia Surabaya 2/10/21 → …

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