The total vertex irregularity strength of symmetric cubic graphs of the Foster's Census

Rika Yanti, Gregory Benedict Tanidi, Suhadi Wido Saputro, Edy Tri Baskoro

Abstract


Foster (1932) performed a mathematical census for all connected symmetric cubic (trivalent) graphs of order n with n ≤ 512. This census then was continued by Conder et al. (2006) and they obtained the complete list of all connected symmetric cubic graphs with order n ≤ 768. In this paper, we determine the total vertex irregularity strength of such graphs obtained by Foster. As a result, all the values of the total vertex irregularity strengths of the symmetric cubic graphs of order n from Foster census strengthen the conjecture stated by Nurdin, Baskoro, Gaos & Salman (2010), namely ⌈(n+3)/4⌉.


Keywords


symmetric cubic graphs, total vertex irregularity strength, algorithms, Foster's census

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DOI: http://dx.doi.org/10.19184/ijc.2022.6.2.3

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