Type 1 Kochol Superpositions: Goldberg and Loupekine with Blowup and Semiblowup snarks

A -total coloring of is an assignment of colors to the vertices and edges of , so that adjacent or incident elements have different colors. The Total Coloring Conjecture (TCC) asserts that a total coloring of a graph has at least and at most colors. In this paper, we determine that all members of new infinite families of snarks obtained by the Kochol superposition of Goldberg and Loupekine with Blowup and Semiblowup snarks are Type~1. These results contribute to a question posed by Brinkmann, Preissmann and D. Sasaki (2015) by presenting negative evidence about the existence of Type~2 cubic graphs with girth at least 5.