Applied Mathematics and Computation, ( ISI ), Volume (364), Year (2020-1) , Pages (124676-124683)

Title : ( Local metric dimension of graphs: Generalized hierarchical products and some applications )

Authors: سندی کلاوژار , 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
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@article{paperid:1075696,
author = {سندی کلاوژار 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},
}

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%0 Journal Article
%T Local metric dimension of graphs: Generalized hierarchical products and some applications
%A سندی کلاوژار
%A Tavakoli, Mostafa
%J Applied Mathematics and Computation
%@ 0096-3003
%D 2020

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