What is the NEPS of Graphs? [Graph Theory]
This video is a re-shoot of my previous video on the NEPS. It introduces the NEPS of graphs and will cover several examples. The NEPS, or non-complete extended p-sum of connected graphs, is a very general graph operation, capable of expressing other graph operations like the tensor, cartesian, and strong products of graphs. It is a generalization of the graph product from graph theory. The NEPS takes as its input an n-tuple of graphs as well as a set of binary n-tuples, known as the basis; the NEPS outputs an undirected graph with some special properties. The output, then, depends not only on the choice of graphs, but also the choice of ordering the graphs, as well as the choice of basis. In this video we will also introduce the concept of distance vector.
If you're interested in learning more about the NEPS of graphs, here are some papers examining the operation in greater depth:
https://core.ac.uk/download/pdf/82010...
https://www.sciencedirect.com/science...
https://www.sciencedirect.com/science...
https://www.sciencedirect.com/science...
https://www.researchgate.net/publicat...
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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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