Title : ( Local metric dimension of graphs: Generalized hierarchical products and some applications )
Authors: Sandi Klavzar , Mostafa Tavakoli ,
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Abstract
Let G be a graph and S⊆V(G). If every two adjacent vertices of G have different metric S-representations, then S is a local metric generator for G. A local metric generator of smallest order is a local metric basis for G, its order is the local metric dimension of G. Lower and upper bounds on the local metric dimension of the generalized hierarchical product are proved and demonstrated to be sharp. The results are applied to determine or bound the dimension of several graphs of importance in mathematical chemistry. Using the dimension, a new model for assigning codes to customers in delivery services is proposed.
Keywords
Metric dimension Local metric dimension Generalized hierarchical product Molecular graph Delivery service
@article{paperid:1075696,
author = {Sandi Klavzar and Tavakoli, Mostafa},
title = {Local metric dimension of graphs: Generalized hierarchical products and some applications},
journal = {Applied Mathematics and Computation},
year = {2020},
volume = {364},
month = {January},
issn = {0096-3003},
pages = {124676--124683},
numpages = {7},
keywords = {Metric dimension
Local metric dimension
Generalized hierarchical product
Molecular graph
Delivery service},
}
%0 Journal Article
%T Local metric dimension of graphs: Generalized hierarchical products and some applications
%A Sandi Klavzar
%A Tavakoli, Mostafa
%J Applied Mathematics and Computation
%@ 0096-3003
%D 2020
