What is the Co-normal Product of Graphs? [Discrete Mathematics]
This video defines the co-normal product (also known as the OR product) of graphs and shows how you to calculate this product yourself, with plenty of examples covered as well.
The co-normal product of graphs is a graph product, that is, it is a binary operation on graphs that takes as its input 2 undirected, simple graphs, and outputs a new undirected simple graph with vertex set equal to the cartesian product of the vertex sets of the factor graphs. The co-normal product of graphs is a 'denser' product than the cartesian or tensor products, as it always results in a graph with more edges than your typical cartesian or tensor graph product. To find the co-normal product of two graphs G and H, take the cartesian product of their vertex sets, with each pair of vertices from G and from H representing a single vertex in the co-normal product of G and H, and then connect these vertices in the co-normal product according to the adjacency rules covered in the video.
The co-normal product is not one of the more common graph products, but it is still an interesting operation to explore and I encourage you to investigate its properties on your own.
See these links for more information:
https://en.wikipedia.org/wiki/Graph_p...
https://www.researchgate.net/figure/T...
https://math.stackexchange.com/questi...
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If you want to learn more about graph products, I highly recommend the following book:
"Handbook of Product Graphs": https://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.
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