TY - JOUR
T1 - A Criterion for (Non-)Planarity of The Block-Transformation Graph Gαβγ when αβγ = 101
AU - Basavanagoud, B.
AU - Veeragoudar, Jaishri B.
JF - Bulletin of Mathematical Sciences and Applications
VL - 10
SP - 38
EP - 47
SN - 2278-9634
PY - 2014
PB - SciPress Ltd
DO - 10.18052/www.scipress.com/BMSA.10.38
UR - https://www.scipress.com/BMSA.10.38
KW - Crossing Number
KW - Minimally Nonouterplanar
KW - Outerplanar
KW - Planar
AB - 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.
ER -