On the planarity of line Mycielskian graph of a graph

Keerthi G. Mirajkar, Anuradha V Deshpande


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.


Planar graph; outerplanar; maximal planar; maximal outerplanar; minimal nonouter planar; 1-planar.

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DOI: http://dx.doi.org/10.23755/rm.v38i0.506


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Ratio Mathematica - Journal of Mathematics, Statistics, and Applications. ISSN 1592-7415; e-ISSN 2282-8214.