What is the Modular Product of Graphs? [Discrete Math]

This video introduces the modular product of graphs, along with 3 visual examples. We will analyze 2 interesting properties of the modular product as well, one with respect to complementation and the other to subgraph isomorphisms of the factor graphs. The modular product of graphs is a graph product based on the cartesian product, where the vertex set is the cartesian product of the vertex sets of the factor graphs, and the edge set is produced through 2 "adjacency rules" or requirements for adjacency. The modular product has been used to transform problems of induced subgraph isomorphism to problems of finding cliques or maximum cliques in graphs.
For more information, see these links:
en.wikipedia.o...
www.sciencedir...
link.springer....
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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/48WKqfy
Note: This is my Amazon Affiliate link. As an Amazon Associate I may earn commissions for purchases made through the link above.

[@atrsankaralingamvalarmathi3]

Very interesting Sir... Thank you 🙏

[@VitalSine]

My pleasure, thank you for watching.

[@atrsankaralingamvalarmathi3]

@@VitalSine Sir, I have a doubt in 1st example that, by the second adjacency rule (b,1) & (c,2), (b,2) &(c,3), (b,2)&(c,1), (a,1)&(c,2),(a,3)&(c,2) should not be adjacent right because a,b not adjacent to c and 1, 2&2,3 are adjacent

[@VitalSine]

@atrsankaralingam valarmathi Good catch, you are correct. I will add a note to the video to point that out. Thanks for letting me know 👍

[@atrsankaralingamvalarmathi3]

@@VitalSine My pleasure Sir... Thank you