On permanent graphs

Quasi-total Graphs with Crossing Numbers

“…A graph G has crossing number 1, if Cr(G)=1. The two to tw conc quasi-total graph P(G) of a graph G is the graph whose point set is V(G) U X(G) and points are adjacent if and only if they correspond to two non adjacent points of G or o ad ent lines of G or one is a point and other is a line incident with it in G. This ept was introduced in [2]. jac The following will be useful in the proof of our results.…”