TY - JOUR

T1 - The fractional local metric dimension of comb product graphs

AU - Aisyah, S.

AU - Utoyo, Mohammad Imam

AU - Susilowati, Liliek

N1 - Publisher Copyright:
© 2020 University of Baghdad. All rights reserved.

PY - 2020/12/1

Y1 - 2020/12/1

N2 - For the connected graph G with vertex set V(G) and edge set E(G), the local resolving neighborhood Rl{u, v} of two adjacent vertices u, v is defined by Rl{u, v} = {x ∈ V(G): d(x, u) ≠ d(x, v)}. A local resolving function fl of G is a real valued function fl: V(G) → [0,1] such that fl(Rl{u, v}) ≥ 1 for every two adjacent vertices u, v ∈ V(G). The fractional local metric dimension of graph G denoted dimfl(G), is defined by dimfl(G) = min{|ftl|: fl is a local resolving function of G}. One of the operation in graph is the comb product graphs. The comb product graphs of G and H is denoted by G < H. The purpose of this research is to determine the fractional local metric dimension of G < H, for graph G is a connected graph and graph H is a complete graph (Kn). The result of G < Kn is dimfl(G < Kn) = |V(G)|. dimfl(Kn−1).

AB - For the connected graph G with vertex set V(G) and edge set E(G), the local resolving neighborhood Rl{u, v} of two adjacent vertices u, v is defined by Rl{u, v} = {x ∈ V(G): d(x, u) ≠ d(x, v)}. A local resolving function fl of G is a real valued function fl: V(G) → [0,1] such that fl(Rl{u, v}) ≥ 1 for every two adjacent vertices u, v ∈ V(G). The fractional local metric dimension of graph G denoted dimfl(G), is defined by dimfl(G) = min{|ftl|: fl is a local resolving function of G}. One of the operation in graph is the comb product graphs. The comb product graphs of G and H is denoted by G < H. The purpose of this research is to determine the fractional local metric dimension of G < H, for graph G is a connected graph and graph H is a complete graph (Kn). The result of G < Kn is dimfl(G < Kn) = |V(G)|. dimfl(Kn−1).

KW - Comb product graphs

KW - Local fractional metric dimension

KW - Resolving function

UR - http://www.scopus.com/inward/record.url?scp=85097503732&partnerID=8YFLogxK

U2 - 10.21123/bsj.2020.17.4.1288

DO - 10.21123/bsj.2020.17.4.1288

M3 - Article

AN - SCOPUS:85097503732

SN - 2078-8665

VL - 17

SP - 1288

EP - 1293

JO - Baghdad Science Journal

JF - Baghdad Science Journal

IS - 4

ER -