On the planarity of line Mycielskian graph of a graph

The line Mycielskian graph of a graph G, denoted by L(G) is defined as the graph obtained from L(G) by adding q + 1 new vertices E0 = e0 i : 1 i q and e, then for 1 i q, joining e0 i to the neighbours of ei and to e. The vertex e is called the root of L(G). This research paper deals with the characterization of planarity of line Mycielskian Graph L(G) of a graph. Further, we also obtain the characterization on outerplanar, maximal planar, maximal outerplanar, minimal nonouterplanar and 1-planar of L(G).