On the planarity of line Mycielskian graph of a graph

The line Mycielskian graph of a graph G, denoted by Lμ(G) is defined as the graph obtained from L(G) by adding q+1 new vertices E' = ei' : 1 ≤  i ≤  q and e, then for 1 ≤  i ≤  q , joining ei' to the neighbours of ei  and  to e. The vertex e is called the root of Lμ(G).  This research paper deals with the characterization of planarity of line Mycielskian Graph Lμ(G) of a graph. Further, we also obtain the characterization on outerplanar, maximal planar, maximal outerplanar, minimally nonouterplanar and 1-planar of Lμ(G).Keywords :  Planar graph, Outerplanar, Maximal planar, Maximal outerplanar, Minimally nonouterplanar and 1-planar.2010 AMS subject classifications : 05C07, 05C10, 05C38, 05C60, 05C76

Characterizations of planar plick graphs

In this paper we present characterizations of graphs whose plick graphs are planar, outerplanar and minimally nonouterplanar