TY - GEN
T1 - On local central monophonic metric dimension of graphs
AU - Lathifah, Ririana Annisatul
AU - Rinurwati, Rinurwati
N1 - Publisher Copyright:
© 2025 Author(s).
PY - 2025/11/6
Y1 - 2025/11/6
N2 - Let Γ be a simple connected graph with vertex set V(Γ) and edge set E(Γ). For u,v ∈ V(Γ), the monophonic distance from u to v is the length of the longest path that does not contain a chord from u to v and is denoted by dm(u,v). A set U ⊆ V(Γ) is called a local central monophonic resolving set if every adjacent vertex in Γ has a distinct monophonic representation with respect to U. The local central monophonic metric dimension, denoted by mdimcl(Γ), is a new perspective in determining the value of the local central metric dimension using the monophonic distance. To determine the value of the local central monophonic metric dimension of a graph, it is first necessary to determine the monophonic central set of the graph. Next, the local monophonic resolving set containing all the monophonic central vertices of the graph is determined. The local central monophonic metric dimension is the minimum cardinality of the local central monophonic resolving set of the graph. This research derives the central local monophonic metric dimension for Pn, Cn, and Sn, denoted by mdimcl(Pn), mdimcl(Cn), and mdimcl(Sn). The central local monophonic metric dimension for the degree-splitting graph of Pn, Cn, and Sn, denoted by mdimcl(DS(Pn)), mdimcl(DS(Cn)), and mdimcl(DS(Sn)) is also given. The result of this paper shows that the monophonic central set of Pn, Cn, and Sn is also the local monophonic resolving set of the graph, but for the degree-splitting graph of Pn, Cn, and Sn, the monophonic central set is not necessarily a local monophonic resolving set for the graph.
AB - Let Γ be a simple connected graph with vertex set V(Γ) and edge set E(Γ). For u,v ∈ V(Γ), the monophonic distance from u to v is the length of the longest path that does not contain a chord from u to v and is denoted by dm(u,v). A set U ⊆ V(Γ) is called a local central monophonic resolving set if every adjacent vertex in Γ has a distinct monophonic representation with respect to U. The local central monophonic metric dimension, denoted by mdimcl(Γ), is a new perspective in determining the value of the local central metric dimension using the monophonic distance. To determine the value of the local central monophonic metric dimension of a graph, it is first necessary to determine the monophonic central set of the graph. Next, the local monophonic resolving set containing all the monophonic central vertices of the graph is determined. The local central monophonic metric dimension is the minimum cardinality of the local central monophonic resolving set of the graph. This research derives the central local monophonic metric dimension for Pn, Cn, and Sn, denoted by mdimcl(Pn), mdimcl(Cn), and mdimcl(Sn). The central local monophonic metric dimension for the degree-splitting graph of Pn, Cn, and Sn, denoted by mdimcl(DS(Pn)), mdimcl(DS(Cn)), and mdimcl(DS(Sn)) is also given. The result of this paper shows that the monophonic central set of Pn, Cn, and Sn is also the local monophonic resolving set of the graph, but for the degree-splitting graph of Pn, Cn, and Sn, the monophonic central set is not necessarily a local monophonic resolving set for the graph.
UR - https://www.scopus.com/pages/publications/105023078851
U2 - 10.1063/5.0302147
DO - 10.1063/5.0302147
M3 - Conference contribution
AN - SCOPUS:105023078851
T3 - AIP Conference Proceedings
BT - AIP Conference Proceedings
A2 - Agustin, Ika Hesti
A2 - Kristiana, Arika Indah
A2 - Nisviasari, Rosanita
A2 - Kurniawati, Elsa Yuli
A2 - Dafik, null
PB - American Institute of Physics
T2 - 8th International Conference on Combinatorics, Graph Theory, and Network Topology, ICCGANT 2024
Y2 - 12 November 2024 through 13 November 2024
ER -