The general concept of the block-transformation graph G^{αβγ} was introduced in [1]. The vertices and blocks of a graph are its members. The block-transformation graph G101 of a graph G is the graph, whose vertex set is the union of vertices and blocks of G, in which two vertices are adjacent whenever the corresponding vertices of G are adjacent or the corresponding blocks of G are nonadjacent or the corresponding members of G are incident. In this paper, we present characterizations of graphs whose block-transformation graphs G^{101} are planar, outerplanar or minimally nonouterplanar. Further we establish a necessary and sufficient condition for the block-transformation graph G^{101} to have crossing number one.

Periodical:

Bulletin of Mathematical Sciences and Applications (Volume 10)

Pages:

38-47

Citation:

B. Basavanagoud and J. B. Veeragoudar, "A Criterion for (Non-)Planarity of The Block-Transformation Graph G^{αβγ} when αβγ = 101", Bulletin of Mathematical Sciences and Applications, Vol. 10, pp. 38-47, 2014

Online since:

November 2014

Authors:

Keywords:

Distribution:

Open Access

This work is licensed under a

Creative Commons Attribution 4.0 International License

References:

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Cited By:

[1] A. Kelarev, W. Susilo, M. Miller, J. Ryan, "Ideals of Largest Weight in Constructions Based on Directed Graphs", Bulletin of Mathematical Sciences and Applications, Vol. 15, p. 8, 2016

DOI: https://doi.org/10.18052/www.scipress.com/BMSA.15.8[2] B. Basavanagoud, V. Kulli, "Qlick Graphs with Crossing Number One", Bulletin of Mathematical Sciences and Applications, Vol. 17, p. 75, 2016

DOI: https://doi.org/10.18052/www.scipress.com/BMSA.17.75