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August 2020 Edge metric dimension of $k$ multiwheel graph
Mohammad S. Bataineh, Nida Siddiqui, Zahid Raza
Rocky Mountain J. Math. 50(4): 1175-1180 (August 2020). DOI: 10.1216/rmj.2020.50.1175

Abstract

If we consider G=(V,E) to be a connected graph, with v V and e=uw E, then dG(e,v)= min{dG(u,v),dG(w,v)} has been defined as the distance between a vertex v and an edge e. The cardinality of the smallest subset SV which can assign a unique distance vector to every edge of G is referred to as edge metric dimension (EMD) given by edim(G). A k multiwheel graph W1,n,k is composed of k cycles Cn along with a central vertex x such that x is adjacent to each of the vertices of C1 and the corresponding vertices of the two consecutive cycles Ci and Ci+1 are also adjacent for all 1i(k1). This article discusses the EMD of the double wheel graph and extends the results to the general k multiwheel graph.

Citation

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Mohammad S. Bataineh. Nida Siddiqui. Zahid Raza. "Edge metric dimension of $k$ multiwheel graph." Rocky Mountain J. Math. 50 (4) 1175 - 1180, August 2020. https://doi.org/10.1216/rmj.2020.50.1175

Information

Received: 9 March 2019; Revised: 16 December 2019; Accepted: 12 January 2020; Published: August 2020
First available in Project Euclid: 29 September 2020

zbMATH: 07261858
MathSciNet: MR4154801
Digital Object Identifier: 10.1216/rmj.2020.50.1175

Subjects:
Primary: 05C12, 05C76, 05C90

Rights: Copyright © 2020 Rocky Mountain Mathematics Consortium

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Vol.50 • No. 4 • August 2020
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