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arXiv · 1509.00842

Large Networks of Diameter Two Based on Cayley Graphs

Marcel Abas
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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 $d\geq 8$, 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 $\frac23$ 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.

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Marcel Abas. 2017-04-20. Large Networks of Diameter Two Based on Cayley Graphs. https://doi.org/10.1007/978-3-319-57264-2_23

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