A construction for a counterexample to the pseudo 2-factor isomorphic graph conjecture

A graph G admitting a 2-factor is pseudo isomorphic if the parity of number cycles in all its 2-factors same. In Abreu et al. (2008) some authors this note gave partial characterisation bipartite cubic graphs and conjectured that K3,3, Heawood Pappus are only essentially 4-edge-connected ones. Goedgebeur (2015) Jan computationally found on 30 vertices which bipartite, cyclically 6-edge-connected, thus refuting above conjecture. note, we describe how such can be constructed from generalised Petersen GP(8,3), Levi Fano 73 configuration Möbius–Kantor 83 configuration, respectively. Such description allows us to understand automorphism group, has order 144, using both geometrical theoretical approach simultaneously. Moreover illustrate uniqueness graph.