Unification of graph products and compatibility with switching
Sho Kubota
TL;DR
This paper introduces a unified framework for various graph products and demonstrates their compatibility with Godsil--McKay switching, enabling new insights into graph transformations such as deriving Doob graphs from Hamming graphs.
Contribution
It defines a unified class of graph products and proves their compatibility with switching, connecting different graph families through switching operations.
Findings
Unified graph products framework established
Compatibility with Godsil--McKay switching proven
Derived Doob graphs from Hamming graphs via switching
Abstract
We define the type of graph products, which enable us to treat many graph products in a unified manner. These unified graph products are shown to be compatible with Godsil--McKay switching. Furthermore, by this compatibility, we show that the Doob graphs can also be obtained from the Hamming graphs by switching.
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Taxonomy
TopicsGraph theory and applications · Advanced Graph Theory Research · Interconnection Networks and Systems