Doubly semi-equivelar maps on the plane and the torus. Issue 3 (2nd September 2022)

• Record Type: Journal Article
• Authors: Singh, Yogendra; Tiwari, Anand Kumar
• Is Part Of: AKCE International Journal of Graphs and Combinatorics. Volume 19:Issue 3(2022)
• Page Start: 296
• Page End: 310
• Publication Date: 2022-09-02
• Subjects: 2-uniform maps -- semi-equivelar maps -- doubly semi-equivelar maps -- torus; 52B70 -- 05C30 -- 05C38
• DOI: 10.1080/09728600.2022.2146549
• Languages: English
• ISSNs: 0972-8600

Abstract

Abstract: A map is called 2-semi equivelar if it has exactly two distinct cyclic arrangement of faces at its vertices. A 2-semi-equivelar map is called 2-uniform if it has precisely 2 orbits of vertices under its symmetric group. Doubly semi-equivelar maps are a subclass of 2-semi equivelar maps that are used to determine 2-uniform maps. In this article, we determine doubly semi-equivelar maps of curvature 0 on the plane and torus exhaustively. Further, we present a classification of doubly semi-equivelar maps on the torus and illustrate this for those doubly semi-equivelar maps which comprise face-sequence pairs { ( 3 6 ), ( 3 3 .4 2 ) } and { ( 3 3 .4 2 ), ( 4 4 ) } .