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Tuite, James
(2018).
DOI: https://doi.org/10.1016/j.dam.2017.10.034
Abstract
An important topic in the design of efficient networks is the construction of (d, k, +Є)- digraphs, i.e. k-geodetic digraphs with minimum out-degree ≥ d and order M(d,k)+ Є, where M(d,k) represents the Moore bound for degree d and diameter k and Є > 0 is the (small) excess of the digraph. Previous work has shown that there are no (2, k,+1)-digraphs for k ≥ 2. In a separate paper, the present author has shown that any (2, k,+2)-digraph must be diregular for k ≥ 2. In the present work, this analysis is completed by proving the nonexistence of diregular (2, k,+2)-digraphs for k ≥ 3 and classifying diregular (2,2,+2)-digraphs up to isomorphism.
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About
- Item ORO ID
- 52980
- Item Type
- Journal Item
- ISSN
- 0166-218X
- Keywords
- Degree/diameter problem; Digraphs; Excess; Extremal digraphs
- Academic Unit or School
-
Faculty of Science, Technology, Engineering and Mathematics (STEM) > Mathematics and Statistics
Faculty of Science, Technology, Engineering and Mathematics (STEM) - Copyright Holders
- © 2017 Elsevier
- Related URLs
- Depositing User
- James Tuite