The Total Vertex Irregularity Strength of Foster^s Census Graph Rikayanti, Suhadi Wido Saputro, Edy Tri Baskoro
Institut Teknologi Bandung
Abstract
Foster (1932) performed a mathematical census for all connected symmetric cubic (trivalent) graphs of order -n- with -n \le 512-.
This census was then continued by Conder et al. (2006) and the last update can be seen in the list he has made up to the -10000- vertices.
%, he continued his list up to 2048 points in 2006. The last update can be seen in the list he has made up to the -10000- vertices.
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 -\lceil (n+3)/4 \rceil-.
Keywords: total vertex irregularity strength, cubic symmetric graph, algorithm, Foster^s Census
