On metric dimension of hs×p hellebores flower graph

P. S. Venkatesh; Archana Bengeri; Prasanna Poojary; Sunny Kumar Sharma

doi:10.1142/S1793830925501010

On metric dimension of h_s×p hellebores flower graph

P. S. Venkatesh
, Archana Bengeri
, Prasanna Poojary
, Sunny Kumar Sharma^*

^*Corresponding author for this work

Department of Mathematics, Manipal Institute of Technology, Bengaluru

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

Abstract

A metric basis is a subset of vertex set in a graph G, such that every vertex in the graph G has a unique distance vector to the vertices in the subset. The cardinality of the metric basis is called the metric dimension of G, and is presented by dim(G). In this paper, we define the hellebores flower graph, and it is denoted by h_s×p. For this graph, we investigate its metric basis as well as the metric dimension, and we also show that it is unbounded and is equal to (s/2 + 1) if s = 2(2t + 1) and ⌈s/2⌉ otherwise.

Original language	English
Article number	2550101
Journal	Discrete Mathematics, Algorithms and Applications
DOIs	https://doi.org/10.1142/S1793830925501010
Publication status	Accepted/In press - 2025

All Science Journal Classification (ASJC) codes

Discrete Mathematics and Combinatorics

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10.1142/S1793830925501010

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abstract = "A metric basis is a subset of vertex set in a graph G, such that every vertex in the graph G has a unique distance vector to the vertices in the subset. The cardinality of the metric basis is called the metric dimension of G, and is presented by dim(G). In this paper, we define the hellebores flower graph, and it is denoted by hs×p. For this graph, we investigate its metric basis as well as the metric dimension, and we also show that it is unbounded and is equal to (s/2 + 1) if s = 2(2t + 1) and ⌈s/2⌉ otherwise.",

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AU - Poojary, Prasanna

AU - Sharma, Sunny Kumar

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AB - A metric basis is a subset of vertex set in a graph G, such that every vertex in the graph G has a unique distance vector to the vertices in the subset. The cardinality of the metric basis is called the metric dimension of G, and is presented by dim(G). In this paper, we define the hellebores flower graph, and it is denoted by hs×p. For this graph, we investigate its metric basis as well as the metric dimension, and we also show that it is unbounded and is equal to (s/2 + 1) if s = 2(2t + 1) and ⌈s/2⌉ otherwise.

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On metric dimension of h_s×p hellebores flower graph

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