Abstract
<p>Foster (1932) performed a mathematical census for all connected symmetric cubic (trivalent) graphs of order <em>n</em> with <em>n </em>≤ 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 <em>n</em> ≤ 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 <em>n</em> from Foster census strengthen the conjecture stated by Nurdin, Baskoro, Gaos &amp; Salman (2010), namely ⌈(<em>n</em>+3)/4⌉.</p>
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