August 2021 Wiener index and addressing of the total graph
M. Gholamnia Taleshani, Ahmad Abbasi
Rocky Mountain J. Math. 51(4): 1453-1462 (August 2021). DOI: 10.1216/rmj.2021.51.1453

Abstract

Graham and Pollak showed that the vertices of any connected graph G can be assigned t-tuples with entries in {0,a,b}, called addresses, such that the distance between any two vertices can be determined from their addresses. In this paper we determine the minimum value of such t, called squashed-cube dimension for the total graph T(Γ(2n pm)) where n,m1 and p3 is a prime number.

Citation

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M. Gholamnia Taleshani. Ahmad Abbasi. "Wiener index and addressing of the total graph." Rocky Mountain J. Math. 51 (4) 1453 - 1462, August 2021. https://doi.org/10.1216/rmj.2021.51.1453

Information

Received: 8 September 2019; Revised: 20 January 2021; Accepted: 22 January 2021; Published: August 2021
First available in Project Euclid: 5 August 2021

MathSciNet: MR4298859
zbMATH: 1472.05041
Digital Object Identifier: 10.1216/rmj.2021.51.1453

Subjects:
Primary: 05C12 , 05C25 , 05C50

Keywords: addressing , distance matrix , eigenvalue , Wiener index

Rights: Copyright © 2021 Rocky Mountain Mathematics Consortium

Vol.51 • No. 4 • August 2021
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