The complement bi-metric dimension of graphs

Jafna Kamalia Sundusia, Rinurwati*

*Corresponding author for this work

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


Given G=(V, E) be a connected graph with vertex set V(G), edge set E(G). For S={s1, s2, s3, ..., sk} ⊂ V(G) and each vertex u∈V(G), we associate a pair of k-dimensional vectors (a, b), with a=(d(u, s1), d(u, s2), ..., d(u, sk)) and b=(δ(u, s1), δ(u, s2), ..., δ(u, sk)), where d(u, sk) and δ(u, sk) respectively denote lengths of a shortest and longest paths between u and sk. If for every two vertices u, v∈V(G) with u≠v resulting in r(u|S)≠r(v|S), then S is a bi-resolving set in G. Bi-metric dimension of G denoted by βb(G) is bi-resolving set S whose cardinality is minimum. The purpose of this study is to develop a new concept of a type of bimetric dimension of a graph G called complement bi-metric dimension of G, βb¯(G), and give exact value of βb¯(G), where G is a graph Pn, Kn, Cn, and Sn, as well as further analyze.

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
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
ISSN (Print)0094-243X
ISSN (Electronic)1551-7616


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


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