ASHISH KUMAR UPADHYAY
Articles written in Proceedings – Mathematical Sciences
Volume 115 Issue 3 August 2005 pp 279-307
Degree-regular triangulations of torus and Klein bottle
Basudeb Datta Ashish Kumar Upadhyay
A triangulation of a connected closed surface is called weakly regular if the action of its automorphism group on its vertices is transitive. A triangulation of a connected closed surface is called degree-regular if each of its vertices have the same degree. Clearly, a weakly regular triangulation is degree-regular. In [8], Lutz has classified all the weakly regular triangulations on at most 15 vertices. In [5], Datta and Nilakantan have classified all the degree-regular triangulations of closed surfaces on at most 11 vertices.
In this article, we have proved that any degree-regular triangulation of the torus is weakly regular. We have shown that there exists an
Volume 118 Issue 2 May 2008 Article ID 2 Errata
On degree-regular triangulations of torus and Klein bottle
Volume 127 Issue 4 September 2017 pp 737-751 Research Article
Hamiltonian cycles in polyhedral maps
DIPENDU MAITY ASHISH KUMAR UPADHYAY
We present a necessary and sufficient condition for existence of a contractible, non-separating and non-contractible separating Hamiltonian cycle in the edge graph of polyhedral maps on surfaces.We also present algorithms to construct such cycles whenever it exists where one of them is linear time and another is exponential time algorithm.
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