TY - GEN

T1 - Local multiset dimension of related cycle graphs

AU - Alfarisi, Ridho

AU - Utoyo, M. Imam

AU - Dafik,

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

PY - 2022/3/24

Y1 - 2022/3/24

N2 - Suppose the set W = {s1, s2,⋯, sk} is a subset of the vertex set V(G). The representation of a vertex v of G with respect to W as follows rm(v|W) = { d(v, s1), d(v, s2), ⋯, d(v, sk)} where d(v, si),1 ≤ i ≤ k is the distance between the vertex v with the vertices of set W together with their multiplicities. The set W is called the m-local resolving set of G if every two adjacent vertices of G have distinct representation with respect to W. If G has an m-local resolving set, then an m-local resolving set having minimum cardinality is called a local multiset basis and its cardinality is called the local multiset dimension of G, denoted by mdl (G). We say that G has an infinite local multiset dimension and we write mdl(G) = ∞. In this paper, we determine the local multiset dimension of related cycle graphs namely kayak paddles graph, and cycles with chord.

AB - Suppose the set W = {s1, s2,⋯, sk} is a subset of the vertex set V(G). The representation of a vertex v of G with respect to W as follows rm(v|W) = { d(v, s1), d(v, s2), ⋯, d(v, sk)} where d(v, si),1 ≤ i ≤ k is the distance between the vertex v with the vertices of set W together with their multiplicities. The set W is called the m-local resolving set of G if every two adjacent vertices of G have distinct representation with respect to W. If G has an m-local resolving set, then an m-local resolving set having minimum cardinality is called a local multiset basis and its cardinality is called the local multiset dimension of G, denoted by mdl (G). We say that G has an infinite local multiset dimension and we write mdl(G) = ∞. In this paper, we determine the local multiset dimension of related cycle graphs namely kayak paddles graph, and cycles with chord.

UR - http://www.scopus.com/inward/record.url?scp=85127989496&partnerID=8YFLogxK

U2 - 10.1063/5.0072516

DO - 10.1063/5.0072516

M3 - Conference contribution

AN - SCOPUS:85127989496

T3 - AIP Conference Proceedings

BT - International Conference on Science and Applied Science, ICSAS 2021

A2 - Purnama, Budi

A2 - Nugraha, Dewanta Arya

A2 - Suparmi, A.

PB - American Institute of Physics Inc.

T2 - 2021 International Conference on Science and Applied Science, ICSAS 2021

Y2 - 6 April 2021 through 6 April 2021

ER -