TY - GEN

T1 - The complement bi-metric dimension of graphs

AU - Sundusia, Jafna Kamalia

AU - Rinurwati,

N1 - Publisher Copyright:
© 2022 Author(s).

PY - 2022/12/19

Y1 - 2022/12/19

N2 - 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.

AB - 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.

UR - http://www.scopus.com/inward/record.url?scp=85145487885&partnerID=8YFLogxK

U2 - 10.1063/5.0131825

DO - 10.1063/5.0131825

M3 - Conference contribution

AN - SCOPUS:85145487885

T3 - AIP Conference Proceedings

BT - 7th International Conference on Mathematics - Pure, Applied and Computation

A2 - Mufid, Muhammad Syifa�ul

A2 - Adzkiya, Dieky

PB - American Institute of Physics Inc.

T2 - 7th International Conference on Mathematics: Pure, Applied and Computation: , ICoMPAC 2021

Y2 - 2 October 2021

ER -