On Neumaier Cayley graphs
Rhys J. Evans, Sergey Goryainov, Grigory Ryabov, Da Zhao
TL;DR
This paper investigates Neumaier Cayley graphs, providing a criterion for their identification, constructing an infinite family with unbounded nexus, and developing an algorithm for their enumeration with computational results.
Contribution
It introduces a new criterion for Neumaier Cayley graphs, constructs an infinite family with unbounded nexus, and presents an enumeration algorithm with computational findings.
Findings
Established a criterion for Neumaier Cayley graphs based on subgroup cosets.
Constructed an infinite family of Neumaier Cayley graphs with unbounded nexus.
Developed and implemented an algorithm for enumerating Neumaier Cayley graphs.
Abstract
In the present paper, we study Neumaier Cayley graphs. First, we give a criterion for a Cayley graph to be a Neumaier graph with a spread given by the cosets of a subgroup. Further, we construct a new infinite family of Neumaier Cayley graphs of unbounded nexus. Finally, we provide an algorithm for enumerating Neumaier Cayley graphs and computational results obtained by this algorithm.
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Taxonomy
TopicsFinite Group Theory Research · Interconnection Networks and Systems · Mathematics and Applications