On Type 2 Snarks and Dot Products

In order to investigate the relationship between snarks and the total colouring, in this paper, we contribute to the work of Brinkmann et al. [J. Comb. Theory Ser. B, 103 (2013) pp. 468-478.] by constructing new Type 2 snarks with girth 4, that can be obtained from dot products of Type 1 snarks. Furthermore, we show that the snarks found by Brinkmann et al. cannot be decomposed in a dot product of two Type 1 snarks.