A labeling of edges and vertices a simple graph \(G(V,E)\) by mapping \(\Lambda :V\left( G \right) \cup E\left( \to \left\{ { 1,2,3, \ldots ,\Psi } \right\}\) provided that any two pair have distinct weights is called an edge irregular total \(\Psi\)-labeling. If \(\Psi\) minimum \(G\) admits -labelling, then the irregularity strength (TEIS) denoted \(\mathrm{tes}\left(G\right).\) In this paper...

<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 then was continued by Conder et al. (2006) and they obtained the complete list ≤ 768. In this paper, we determine total vertex irregularity strength such Foster. As result, values strengths from Foster strengthen conj...