Large Networks of Diameter Two Based on Cayley Graphs

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.

9 pages, Published in Cybernetics and Mathematics Applications in Intelligent Systems

References in corpus (2)

• Diameter 2 Cayley Graphs of Dihedral Groups
• Cayley graphs of diameter two with order greater than 0.684 of the Moore bound for any degree

Cited by in corpus (1)

• Cayley graphs of diameter two with order greater than 0.684 of the Moore bound for any degree