Can anybody tell me what the current situation in the hierarchical product of graphs is?

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Joseph Varghese Kureethara

Read R. Hammack et al., Handbook of Product Graphs, CRC Press, 2011

Prasanth G. Narasimha-Shenoi

@Joseph Yeah, I had that, I want to know anything more???

Sriram Vaidyanathan

Read articles by L. Barrière for more information and recent developments

Elliot Krop

Hello. If you are still interested in the hierarchical product, there has recently been some work on how the domination number of the product graph is related to the domination number of the factor graphs. This is related to an old open conjecture of Vizing. Here's a link to the paper on Science Direct: Article Domination in the hierarchical product and Vizing’s conjecture