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A Criterion for (Non-)Planarity of The Block-Transformation Graph G<sup>αβγ</sup> when αβγ = 101
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A Criterion for (Non-)Planarity of The Block-Transformation Graph Gαβγ when αβγ = 101

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Abstract:

The general concept of the block-transformation graph Gαβγ 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 G101 are planar, outerplanar or minimally nonouterplanar. Further we establish a necessary and sufficient condition for the block-transformation graph G101 to have crossing number one.

Info:

Periodical:
Bulletin of Mathematical Sciences and Applications (Volume 10)
Pages:
38-47
DOI:
https://doi.org/10.18052/www.scipress.com/BMSA.10.38
Citation:
B. Basavanagoud and J. B. Veeragoudar, "A Criterion for (Non-)Planarity of The Block-Transformation Graph Gαβγ when αβγ = 101", Bulletin of Mathematical Sciences and Applications, Vol. 10, pp. 38-47, 2014
Online since:
November 2014
Authors:
B. Basavanagoud, Jaishri B. Veeragoudar
Keywords:
Crossing Number, Minimally Nonouterplanar, Outerplanar, Planar
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Distribution:
Open Access

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References:

B. Basavanagoud, H. P. Patil and Jaishri B. Veeragoudar, On the block-transformation graphs, graph-equations and diameters, International Journal of Advances in Science and Technology, Vol. 2, No. 2, (2011), 62-74.

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V. R. Kulli, On minimally nonouterplanar graphs, Proc. Indian Nat. Sci. Acad., Vol. 41A(1975), pp.275-280.

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V. R. Kulli and H. P. Patil, Minimally nonouterplanar graphs and some graph valued functions, Karnatak Univ. Sci. J., Vol. 21(1976), pp.123-129.

V. R. Kulli and M. H. Muddebihal, Total-block graphs and semitotal-block graphs with crossing numbers, Far East J. Appl. Math. 4(1)(2000), 99-106.

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