@article{basavanagoud2014,
author = {Basavanagoud, B. and Veeragoudar, Jaishri B.},
title = {A Criterion for (Non-)Planarity of The Block-Transformation Graph G$\alpha$$\beta$$\gamma$ when $\alpha$$\beta$$\gamma$ = 101},
year = {2014},
month = {11},
volume = {10},
pages = {38--47},
journal = {Bulletin of Mathematical Sciences and Applications},
doi = {10.18052/www.scipress.com/BMSA.10.38},
keywords = {Planar, Outerplanar, Minimally Nonouterplanar, Crossing Number},
abstract = {The general concept of the block-transformation graph G$\alpha$$\beta$$\gamma$ 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.}
}