Graphs with the n‐e.c. adjacency property constructed from resolvable designs |
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| Authors: | Catharine A Baker Anthony Bonato Neil A McKay Pawe? Pra?at |
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| Institution: | 1. Department of Mathematics and Computer Science, Mount Allison University, Sackville, NB, Canada E4L 1E6;2. Department of Mathematics, Ryerson University, Toronto, Ont., Canada M5B 2K3;3. Department of Mathematics and Statistics, Dalhousie University, Halifax, NS, Canada B3H 3J5 |
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| Abstract: | Only recently have techniques been introduced that apply design theory to construct graphs with the n‐e.c. adjacency property. We supply a new random construction for generating infinite families of finite regular n‐e.c. graphs derived from certain resolvable Steiner 2‐designs. We supply an extension of our construction to the infinite case, and thereby give a new representation of the infinite random graph. We describe a family of deterministic graphs in infinite affine planes which satisfy the 3‐e.c. property. © 2009 Wiley Periodicals, Inc. J Combin Designs 17: 294–306, 2009 |
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| Keywords: | graphs resolvable designs adjacency properties n‐e c graphs random graphs Steiner 2‐designs affine planes |
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