2005/06/30 by Basudeb Datta, Datta, Basudeb · 2 citations
Computer Science · Engineering · Mathematics · #51M20 #52B70 #57M20 #Advanced Graph Theory Research #Combinatorics (math.CO) #FOS: Mathematics #Finite Group Theory Research #Geometric Topology (math.GT) #graph theory and CDMA systems #math.CO #math.GT #msc:51M20 #msc:52B70 #msc:57M20
paper · pdf · doi:10.48550/arxiv.math/0506618
7 pages. To appear in `Contributions to Algebra and Geometry'
arxiv created 2005/06/30 · openalex publication_date 2005/06/30 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
A polyhedral map is called \p, q\-equivelar if each face has p edges and each vertex belongs to q faces. In 1983, it was shown that there exist infinitely many geometrically realizable \p, q\-equivelar polyhedral maps if q > p = 4, p > q = 4 or q - 3 > p = 3. It was shown in 2001 that there exist infinitely many \4, 4\- and \3, 6\-equivelar polyhedral maps. In 1990, it was shown that \5, 5\- and \6, 6\-equivelar polyhedral maps exist. In this note, examples are constructed, to show that infinitely many self dual \k, k\-equivelar polyhedral maps exist for each k ≥ 5. Also vertex-minimal non-singular \p, p\-pattern are constructed for all odd primes p.