What are Projections and Layers in Graph Products? [Graph Theory]

This video introduces projections and layers of graph products, with plenty of visual examples. We will go over some of the properties of projections and layers as well. A projection is a function from the vertex set of a graph product to the vertex set of one of its factors, while a layer is a set of vertices in a graph product with certain coordinates held fixed and a single coordinate allowed to vary.
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If you want to learn more about graph products, I highly recommend the following book:
"Handbook of Product Graphs": amzn.to/3HjF5D8
Note: This is my Amazon Affiliate link. As an Amazon Associate I may earn commissions for purchases made through the link above.
#graphtheory

[@veerendrakumar]

Thank you so much, sir. Lots of love and respect to you from India ❤

[@thecyberlocal]

Your videos are fascinating. I wanted to solve the exercise but I'm not smart enough yet. I would LOVE it if you made a prep course in graph theory to teach it to people who haven't taken college, so they are ready for your videos. Regardless, you're awesome!

[@VitalSine]

Thank you so much for the kind words! It's a great idea to make a prep course, I haven't been able to make any new videos recently, but I'll definitely make more preparatory content in the near future. I also wanted to let you know I have a couple of introductory graph theory videos on the channel in case you haven't studied introductory graph theory and have not found them yet, but there is definitely more to be done along the lines of prerequisite content. Also, I'm not sure what level of mathematics you are studying right now, but if you're interested, a great textbook for all the prerequisites of graph theory would be "Discrete Mathematics" by Susanna Epp, it's a very good introduction to logic, sets, functions, combinatorics, (a whole bunch of other concepts too) and also has a section introducing graph theory. If you want to get into the math that graph operations, such as graph products, are built from, see the book "A Book of Abstract Algebra" by Pinter, that book is fantastic and if you like graph products you will quickly see the relevance to graph theory while reading it.