Bounds for metric dimensions of generalized neighborhood corona graphs

S. E. Setiawan; Slamin

doi:10.1016/j.heliyon.2021.e07433

Bounds for metric dimensions of generalized neighborhood corona graphs

Rinurwati^*
, S. E. Setiawan
, Slamin

^*Corresponding author for this work

University of Jember

Research output: Contribution to journal › Article › peer-review

2 Citations (Scopus)

Abstract

In this paper, the authors analysed metric dimensions of arbitrary graphs G★˜∧_i=1^|V(G)|H_i in which graphs G,H₁,H₂,…,H_|V(G)| are non-trivial, G is connected, and ★˜ denotes generalized neighborhood corona operation. We found lower bounds of dim(G★˜∧_i=1^|V(G)|H_i) as function of dim_A(H_i) where dim_A(H_i) denotes adjacency metric dimensions of H_i. We also found upper bounds of dim(G★˜∧_i=1^|V(G)|H_i) when G does not contain pair of false twin vertices. Furthermore, we found a characteristic of dim(G★˜∧_i=1^|V(G)|H_i) which indicates that our lower bounds are strict.

Original language	English
Article number	e07433
Journal	Heliyon
Volume	7
Issue number	7
DOIs	https://doi.org/10.1016/j.heliyon.2021.e07433
Publication status	Published - Jul 2021

Keywords

Metric dimension
Neighborhood corona graph
Resolving set

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10.1016/j.heliyon.2021.e07433

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title = "Bounds for metric dimensions of generalized neighborhood corona graphs",

abstract = "In this paper, the authors analysed metric dimensions of arbitrary graphs G★˜∧i=1|V(G)|Hi in which graphs G,H1,H2,…,H|V(G)| are non-trivial, G is connected, and ★˜ denotes generalized neighborhood corona operation. We found lower bounds of dim(G★˜∧i=1|V(G)|Hi) as function of dimA(Hi) where dimA(Hi) denotes adjacency metric dimensions of Hi. We also found upper bounds of dim(G★˜∧i=1|V(G)|Hi) when G does not contain pair of false twin vertices. Furthermore, we found a characteristic of dim(G★˜∧i=1|V(G)|Hi) which indicates that our lower bounds are strict.",

keywords = "Metric dimension, Neighborhood corona graph, Resolving set",

author = "Rinurwati and Setiawan, \{S. E.\} and Slamin",

note = "Publisher Copyright: {\textcopyright} 2021 The Authors",

year = "2021",

month = jul,

doi = "10.1016/j.heliyon.2021.e07433",

language = "English",

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T1 - Bounds for metric dimensions of generalized neighborhood corona graphs

AU - Rinurwati,

AU - Setiawan, S. E.

AU - Slamin,

PY - 2021/7

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N2 - In this paper, the authors analysed metric dimensions of arbitrary graphs G★˜∧i=1|V(G)|Hi in which graphs G,H1,H2,…,H|V(G)| are non-trivial, G is connected, and ★˜ denotes generalized neighborhood corona operation. We found lower bounds of dim(G★˜∧i=1|V(G)|Hi) as function of dimA(Hi) where dimA(Hi) denotes adjacency metric dimensions of Hi. We also found upper bounds of dim(G★˜∧i=1|V(G)|Hi) when G does not contain pair of false twin vertices. Furthermore, we found a characteristic of dim(G★˜∧i=1|V(G)|Hi) which indicates that our lower bounds are strict.

AB - In this paper, the authors analysed metric dimensions of arbitrary graphs G★˜∧i=1|V(G)|Hi in which graphs G,H1,H2,…,H|V(G)| are non-trivial, G is connected, and ★˜ denotes generalized neighborhood corona operation. We found lower bounds of dim(G★˜∧i=1|V(G)|Hi) as function of dimA(Hi) where dimA(Hi) denotes adjacency metric dimensions of Hi. We also found upper bounds of dim(G★˜∧i=1|V(G)|Hi) when G does not contain pair of false twin vertices. Furthermore, we found a characteristic of dim(G★˜∧i=1|V(G)|Hi) which indicates that our lower bounds are strict.

KW - Metric dimension

KW - Neighborhood corona graph

KW - Resolving set

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DO - 10.1016/j.heliyon.2021.e07433

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VL - 7

JO - Heliyon

JF - Heliyon

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ER -

Bounds for metric dimensions of generalized neighborhood corona graphs

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