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LC Kinsey (1993)
Topology of Surfaces
(1982)
https://doi.org/10.1093/qmath/33.4.451 Kinsey, L.C.: Topology of Surfaces
Harish Doraiswamy, V. Natarajan (2013)
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Surgeries of pairing of Edges associated to trivalent graphsBulletin of the Brazilian Mathematical Society, New Series, 47
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Rachid Khoury, Jean-Philippe Vandeborre, Mohamed Daoudi (2013)
3D-Model Retrieval Using Bag-of-Features Based on Closed Curves
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In this paper, we define the concept of graph extension, embedded on a closed and orientable surface, associated to a pairing of edges of regular polygons in order to show that the K -regular pairing of edges graphs can be obtained by the canonical extension of graphs (graphs with a single vertex). We will present examples of K -regular graphs associated to surfaces with genus g ≤ 3. Keywords Trivalent graphs · Closed surfaces · Pairing of edges · Surgeries Mathematics Subject Classification 14J80 · 57M15 · 57N05 1 Introduction Given a polygon P with 2E sides, always is possible to obtain a closed orientable surface M by edge pairing (quotient map), where the image of the border of P corresponds to a graph G with E edges embedded on M (see Fig. 1). Some authors have searched graphs that can be associated with an edge pairing and possible edge pairings linked to each of them. Jorgensen and Naatanen (1982) showed that for E = 9, there are eight trivalent pairings (all vertices have degree 3) for surfaces with genus g = 2. These pairings are associated with five non-isomorphic graphs (see Fig. 12). For g = 3, Nakamura
Bulletin of the Brazilian Mathematical Society, New Series – Springer Journals
Published: Jul 31, 2019
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