2-Metric Dimension of Cartesian Product of Graphs

Geetha, K.; Sooryanarayana, B.

doi:10.12732/ijpam.v112i1.2

Cited by 3 publications

(3 citation statements)

References 2 publications

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“…Then in 2016 Estrada-Moreno et al [2] have found -metric dimension on the corona operation between two graphs. In 2017 Geetha and Sooryanarayana [9] have found the -metric dimension in the graph of cartesian product operation results. In 2018 Rahmadi and Susanti [3] have found the -metric dimension in double fan graph, double conesgraph, double fan snake graph, centralized double fan graph, generalized parachute graph, and generalized parachute graph with the upper path.…”

Section: Introductionmentioning

confidence: 99%

The k-Metric Dimension of Nk + Pn Graph and Starbarbell Graph

Saidah¹,

Kusmayadi²

2020

Proceedings of the SEMANTIK Conference of Mathematics Education (SEMANTIK 2019)

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Let be a simple connected graph with a set of vertices ( ) and set of edges ( ). The distance between two vertices and in a graph are the shortest path length between two vertices and denoted by ( , ). Let be a positive integer, ⊆ with is a -metric generator if and only if for each different vertex pair , ∈ there are at least vertices 1 , 2 , … , ∈ and fulfill ( , ) ≠ ( , ) with ∈ {1, 2, … , }. Minimum cardinality of a -metric generator of a graph is called the basis -metric of graph . The number of elements on the basis of -metric graph are called -metric dimension of graph and denoted by ( ). + is the result of a join operation between null graph and path graph with , ≥ 2. Starbarbell graph denoted by 1, 2,…, is a graph formed from a star graph 1, and complete graph then merge one vertex from each with ℎ leaf of 1, with ≥ 3, 1 ≤ ≤ , and ≥ 2. In this paper, we determine the -metric dimension of + graph and starbarbell graph.

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Section: Introductionmentioning

confidence: 99%

The k-Metric Dimension of Nk + Pn Graph and Starbarbell Graph

Saidah¹,

Kusmayadi²

2020

Proceedings of the SEMANTIK Conference of Mathematics Education (SEMANTIK 2019)

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“…In 2016, Estrada-Moreno et al [5] discovered the kmetric dimension of corona product graphs. In 2017, Geetha and Sooryanarayana [6] discovered the 2-metric dimension of Cartesian product graphs. In 2017, Yero et al [7] investigated computing the k-metric dimension of a graphs.…”

Section: Introductionmentioning

confidence: 99%

On the k-Metric Dimension of a Barbell Graph and a t-fold Wheel Graph

Setyawan¹,

Kusmayadi²

2020

Proceedings of the SEMANTIK Conference of Mathematics Education (SEMANTIK 2019)

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Let G be a connected and simple graph with the vertex set V(G) and the edge set E(G). The set S ⊆ V (G) is called a k-metric generator for G if and only if for every two pairs different vertices u,v ∈ V(G), there are at least k vertices w1,w2, . . .,wk ∈ S such that d(u,wi) ≠ d(v,wi) for every i ∈ {1, 2, …, k}, with d(u,v) is the length of shortest uv path. A minimum k-metric generator is called a k-metric basis and its cardinality is called the k-metric dimension of G, denoted by dimk(G). A barbell graph Bn,n for n ≥ 3 is the simple graph obtained from two complete graph Kn connected by a bridge. A t-fold wheel graph Wnt for t ≥ 2 and n ≥ 3 is the simple graph that contain the central t vertex which are adjacent to each vertex in a cycle, but not adjacent to each other. In this paper, we determine the kmetric dimension of a barbell graph and a t-fold wheel graph.

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“…In 2016, Estrada Moreno et al [2] have found the k-metric dimension on the corona operation of two graphs. In 2017 Geetha and Sooryanarayana [6] have found the k-metric dimension in the graph of cartesian product operation result. In 2018 Rahmadi and Susanti [7] found the k-metric dimension in double fan graph, double cones graph, double fan snake graph, centralized double fan graph, generalized parachute graph, and graph parachute generalized with the upper path.…”

Section: Introductionmentioning

confidence: 99%

k-Metric Dimension of Generalized Fan Graph and Cm ∗2 Kn Graph

Hidayah¹,

Kusmayati²

2020

Proceedings of the SEMANTIK Conference of Mathematics Education (SEMANTIK 2019)

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Let G be a simple connected graph with the vertex set V(G) and the set edge E(G). The set S ⊆ V(G) is called the kmetric generator on G if and only if every two different vertices in G are distinguished by at least k elements in S, in other words for every two different vertices u, v ∈ V(G), there are at least k vertices w 1 , w 2 , … , w k ∈ S such that d(u, w i ) ≠ d(v, w i ), for every i ∈ {1, … , k}. The k-metric generator with the smallest cardinality is called the k-metric base and the cardinality of the k-metric base is on call the k-metric dimension of the graph G denoted dim k (G). In this study, the k-metric dimension was obtained in generalized fan F m,n graph with m ≥ 1, n ≥ 3 and C m * 2 K n graph with m ≥ 3, n ≥ 2.

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2-Metric Dimension of Cartesian Product of Graphs

Cited by 3 publications

References 2 publications

The k-Metric Dimension of Nk + Pn Graph and Starbarbell Graph

The k-Metric Dimension of Nk + Pn Graph and Starbarbell Graph

On the k-Metric Dimension of a Barbell Graph and a t-fold Wheel Graph

k-Metric Dimension of Generalized Fan Graph and Cm ∗2 Kn Graph

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