A Criterion for (Non-)Planarity of The Block-Transformation Graph Gαβγ when αβγ = 101
2014 ◽
Vol 10
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pp. 38-47
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Keyword(s):
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.
2019 ◽
Vol 18
(01)
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pp. 1950006
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2013 ◽
Vol Vol. 15 no. 2
(Combinatorics)
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2019 ◽
Vol 19
(05)
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pp. 2050084
2017 ◽
Vol E100.A
(12)
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pp. 2764-2775
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