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Published in:
2017 | OriginalPaper | Chapter
Large Networks of Diameter Two Based on Cayley Graphs
Author : Marcel Abas
Published in: Cybernetics and Mathematics Applications in Intelligent Systems
Publisher: Springer International Publishing
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Abstract
In this contribution we present a construction of large networks of diameter two and of order \(\frac{1}{2}d^2\) for every degree \(d\ge 8\), based on Cayley graphs with surprisingly simple underlying groups. For several small degrees we construct Cayley graphs of diameter two and of order greater than \(\frac{2}{3}\) of Moore bound and we show that Cayley graphs of degrees \(d\in \{16,17,18,23,24,31,\dots ,35\}\) constructed in this paper are the largest currently known vertex-transitive graphs of diameter two.
