On the planarity of line Mycielskian graph of a graph

Authors

DOI:

https://doi.org/10.23755/rm.v38i0.506

Keywords:

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

Abstract

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.

References

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K. G. Mirajkar and Veena Mathad, THE LINE MYCIELSKIAN GRAPH OF A GRAPH, International Journal of Research and Analytical Reviews(IJRAR), 6(1), (2019), 277-280.

K. G. Mirajkar, Veena Mathad and Pooja B, Miscellaneous Properties of Line Mycielskian Graph of a Graph, International Jopurnal of Applied Engineering Research, 14(29), (2019), 4552-4556.

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Published

2020-06-30

Issue

Vol. 38 (2020)

Section

Volume 38-2020

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