The complement-edge dimension of corona graphs

Rinurwati*, Nirmala Mega Rosyidah

*Corresponding author for this work

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


In this study, a new concept is introduced, namely the complement-edge dimension. This concept is formed from the combination of edge metric dimension and complement metric dimension concepts. Given a connected graph G = (V(G), E(G)) with V(G) = {v1, v2,..., vn }, and an ordered set Q = {q1,..., qk} ⊆ V (G). The representation of the edge e = xy ∈ E (G) with respect to Q can be written as r (e│Q) = (d(e, qi)) = (min{d(x, qi), d (y, qi)}) with explanation d (x, qi) and d (y, qi) state the distance from vertex x to qi and from vertex y to qi for i ∈ {l,2,, k }, respectively. If there are at least two edges in G that have the same representation with respect to Q, that is the definition of a complement-edge generator set of G. The maximum cardinality of set Q is called a complement-edge basis. Further, the number of vertices of the complement-edge basis Q is called a complement-edge dimension of G, known as edim¯ (G). As a main result, the complement-edge dimension that is implemented in corona graphs between a connected graph G and any graph H is found, denoted edim¯(G⊙H). In addition, we also found the upper and lower bound of the edim¯ (G).

Original languageEnglish
Title of host publicationAIP Conference Proceedings
EditorsLathiful Anwar, Desi Rahmadani, Denis Eka Cahyani, Tomi Listiawan, Imam Rofiki, Puguh Darmawan, Andi Daniah Pahrany
PublisherAmerican Institute of Physics Inc.
ISBN (Electronic)9780735448285
Publication statusPublished - 2 Feb 2024
Event3rd International Conference on Mathematics and its Applications, ICoMathApp 2022 - Virtual, Online
Duration: 23 Aug 202224 Aug 2022

Publication series

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


Conference3rd International Conference on Mathematics and its Applications, ICoMathApp 2022
CityVirtual, Online


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