semientire graph; vertex-semientire graph; edge-semientire graph; crossing number; forbidden subgraph; homeomorphic graphs
The purpose of this paper is to give characterizations of graphs whose vertex-semientire graphs and edge-semientire graphs have crossing number 2. In addition, we establish necessary and sufficient conditions in terms of forbidden subgraphs for vertex-semientire graphs and edge-semientire graphs to have crossing number 2.
 V. R. Kulli, D. G. Akka: On semientire graphs
. J. Math. Phys. Sci. 14 (1980), 585–588. MR 0644066
 V. R. Kulli, M. H. Muddebihal: Semientire graphs with crossing number 1. (to appear).