Metric dimension of generalized wheels

Sooryanarayana, B.; Kunikullaya, Shreedhar; Swamy, Narahari Narasimha

doi:10.1016/j.ajmsc.2019.04.002

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K-metric Dimension1

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Cited by 9 publications

(9 citation statements)

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“…However, nothing more had been made so far on this issue. On the other hand, this concept might not be confused with that one, also called k-metric dimension, introduced in [178], which is in fact a very different parameter.…”

Section: K-metric Dimensionmentioning

confidence: 99%

Metric dimension related parameters in graphs: A survey on combinatorial, computational and applied results

Kuziak,

Yero

2021

Preprint

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Section: K-metric Dimensionmentioning

confidence: 99%

Metric dimension related parameters in graphs: A survey on combinatorial, computational and applied results

Kuziak,

Yero

2021

Preprint

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“…These sets and dimensions have been studied for paths and cycles in [1]. Related work can be found in [2][3][4][5][6][7][8][9][10][11][12][13][14][15][16][17][18][19]. For the terms not defined here we refer to [20,22].…”

Section: Introductionmentioning

confidence: 99%

Graphs of Neighborhood Metric Dimension Two

Sooryanarayana¹,

Shanmukha

2021

J. Math. Fund. Sci.

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A subset of vertices of a simple connected graph is a neighborhood set (n-set) of G if G is the union of subgraphs of G induced by the closed neighbors of elements in S. Further, a set S is a resolving set of G if for each pair of distinct vertices x,y of G, there is a vertex s∈ S such that d(s,x)≠d(s,y). An n-set that serves as a resolving set for G is called an nr-set of G. The nr-set with least cardinality is called an nr-metric basis of G and its cardinality is called the neighborhood metric dimension of graph G. In this paper, we characterize graphs of neighborhood metric dimension two.

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“…Slater [10] under the term locating set. For more works on metric dimension, we refer [3,4,6,8,9,11,12,7,14]. The resolving property and dominating property of a network are super hereditary in nature and both are essential for unique identification of the nodes in the network for various purposes.…”

Section: Introductionmentioning

confidence: 99%

Certain Varieties of Resolving Sets of A Graph

Sooryanarayana¹,

Suma²,

Chandrakala³

2021

JIMS

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Let G=(V,E) be a simple connected graph. For each ordered subset S={s_1,s_2,...,s_k} of V and a vertex u in V, we associate a vector Gamma(u/S)=(d(u,s_1),d(u,s_2),...,d(u,s_k)) with respect to S, where d(u,v) denote the distance between u and v in G. A subset S is said to be resolving set of G if Gamma(u/S) not equal to Gamma(v/S) for all u, v in V-S. The purpose of this paper is to introduce various types of r-sets and compute minimum cardinality of each set, in possible cases, particulary for paths, cycles, complete graphs and wheels.

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Metric dimension of generalized wheels

Cited by 9 publications

References 4 publications

Metric dimension related parameters in graphs: A survey on combinatorial, computational and applied results

Metric dimension related parameters in graphs: A survey on combinatorial, computational and applied results

Graphs of Neighborhood Metric Dimension Two

Certain Varieties of Resolving Sets of A Graph

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