What is the NEPS of Graphs? [Graph Theory]

This video 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/82010718.pdf https://www.sciencedirect.com/science/article/pii/S0024379500000616#bBIB5 https://www.sciencedirect.com/science/article/pii/S0012365X00001606 https://www.sciencedirect.com/science/article/pii/S0024379502003221 https://www.researchgate.net/publication/256050903_GCD-graphs_and_NEPS_of_complete_graphs ... https://www.youtube.com/watch?v=E9nPnNfCmJA