On the metric dimension of generalized Petersen graphs

Ahmad, Shabbir; Chaudhry, Muhammad Anwar; Javaid, Imran; Salman, Muhammad

doi:10.2989/16073606.2013.779957

Cited by 20 publications

(15 citation statements)

References 10 publications

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“…In 2008, Javaid et al initiated the study of constant metric index by investigating it for three families of regular networks, and asked for the investigation of more such families possessing the constant metric index [9]. In this regard, a number of research articles have been published on various families of regular networks such as families of Harary networks, Caylay networks, circulant networks, generalized Petersen networks fullerence networks, to name a few [6], [7], [9], [17], [26]- [31]. With this article, we extend the study of constant metric index by exploring one more family of regular networks, namely a family of choral ring networks CR η (1, 3, 5).…”

Section: B Chordal Ring Networkmentioning

confidence: 99%

An Algorithmic Approach to Compute the Metric Index of Chordal Ring Networks

et al. 2020

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The metric is a non-negative assignment to the pairs of nodes in a connected network N , which assigns the number of links lying in a smallest path between the nodes in the pairs. A pair (a, b) of nodes in N is said to be uniquely identified by a node c of N if the metric assigned to the pair (a, c) is different from the metric assigned to the pair (b, c). The metric index of N is the minimum number of nodes in N chosen in such a manner that every two nodes in N are uniquely identified by a chosen node. It is said to be constant for a family of networks if it remains unchange with the extension in the networks. In this paper, we consider a family of chordal ring networks and propose an algorithm which assistances in proving, with the aid of mathematical induction and the concept of good nodes, that there is no change in the metric index of chordal ring networks with the extension in the networks. INDEX TERMS Metric, metric index, chordal ring networks, good node.

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Section: B Chordal Ring Networkmentioning

confidence: 99%

An Algorithmic Approach to Compute the Metric Index of Chordal Ring Networks

et al. 2020

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“…Figure 2. Generalized Petersen graph GP (10,2) WEAKLY CONVEX AND CONVEX DOMINATION NUMBERS 443 1.1. Previous work.…”

Section: Jozef Kratica Dragan Matić and Vladimir Filipovićmentioning

confidence: 99%

“…where the subscripts are taken modulo n, as we will be doing hereafter. The Petersen graph from Example 1.2 is GP (5,2).…”

Section: Generalized Petersen Graphsmentioning

confidence: 99%

Weakly convex and convex domination numbers for generalized Petersen and flower snark graphs

Kratica¹,

Matić²,

Filipović³

2020

Rev. Un. Mat. Argentina

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“…al studied L(2,1) labeling of generalized Petersen graphs [6]. In 2013, Ahmad et al [1] investigated the metric dimension of generalized Petersen graphs.…”

Section: An Overview Of the Papermentioning

confidence: 99%

On strong rainbow vertex-coloring of generalized Petersen graphs G(n,2) and G(n,3)

Arputhamary¹,

Mercy²

2017

ijma

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A path in a vertex-colored graph G is called a rainbow path if no two internal vertices get the same color. A vertex-colored graph G is strongly rainbow vertexconnected, if for every pair of distinct vertices, there exists at least one shortest rainbow path. The minimum number of colors required to strongly rainbow vertex color a graph G is called the strong rainbow vertex-connection number, denoted by srvc(G) .This work presents the exact values of strong rainbow vertexconnection numbers for the generalized Petersen graphs G(n,2) and G(n,3) .

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On the metric dimension of generalized Petersen graphs

Cited by 20 publications

References 10 publications

An Algorithmic Approach to Compute the Metric Index of Chordal Ring Networks

An Algorithmic Approach to Compute the Metric Index of Chordal Ring Networks

Weakly convex and convex domination numbers for generalized Petersen and flower snark graphs

On strong rainbow vertex-coloring of generalized Petersen graphs G(n,2) and G(n,3)

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