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Equivalent nondegenerate L‐shapes of double‐loop networks
Author(s) -
Chen Chiuyuan,
Hwang F.K.
Publication year - 2000
Publication title -
networks
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.977
H-Index - 64
eISSN - 1097-0037
pISSN - 0028-3045
DOI - 10.1002/1097-0037(200009)36:2<118::aid-net7>3.0.co;2-1
Subject(s) - rectangle , loop (graph theory) , transformation (genetics) , algebraic number , mathematics , geometric transformation , double loop , combinatorics , topology (electrical circuits) , discrete mathematics , pure mathematics , computer science , geometry , mathematical analysis , image (mathematics) , artificial intelligence , biochemistry , chemistry , process management , business , gene
Double‐loop networks have been widely studied as architecture for local area networks. The L‐shape is an important tool for studying the distance properties of double‐loop networks. Two L‐shapes are equivalent if the numbers of nodes k steps away from the origin are the same for every k . Hwang and Xu first studied equivalent L‐shapes through a geometric operation called 3‐rectangle transformation. Fiol et al. proposed three equivalent transformations. Rödseth gave an algebraic operation, which was found by Huang et al. to correspond to 3‐rectangle transformations. In this paper, we show that all equivalent nondegenerate L‐shapes are determined by four basic geometric operations. We also discuss the algebraic operations corresponding to these geometric operations. © 2000 John Wiley & Sons, Inc.