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

Rika Yanti (Institut Teknologi Bandung Universitas Singaperbangsa Karawang)
Gregory Benedict Tanidi (Undergraduate Program of Mathematics, Faculty of Mathematics and Natural Sciences, Institut Teknologi Bandung, Indonesia)
Suhadi Wido Saputro (Combinatorial Mathematics Research Group, Faculty of Mathematics and Natural Sciences, Institut Teknologi Bandung, Indonesia)
Edy Tri Baskoro (Combinatorial Mathematics Research Group, Faculty of Mathematics and Natural Sciences, Institut Teknologi Bandung, Indonesia Center for Research Collaboration on Graph Theory and Combinatorics, Indonesia)

Indonesian Journal of Combinatorics
Vol 6, No 2 (2022)

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⌉.