Intro to P-sum, Extended P-sum, and NEPS of Graphs [Graph Theory]

This video covers the graph operations known as p-sum, extended p-sum, and NEPS (non-extended p-sum). Each of these operations takes an ordered n-tuple of graphs as input, and outputs a graph with vertex set equal to the cartesian product of the input graph's vertex sets. However, these operations differ in how their edge sets are defined. The NEPS is the most general of these operations and contains the other two as special cases. The p-sum is the least general of these operations and is a special case of both the NEPS and the extended p-sum. These operations can be used to represent certain graph products (cartesian, tensor, strong products), but are more general than graph products as well.
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Links for more information:
www.jstor.org/...
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[@Alirazakb]

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[@VitalSine]

You're very welcome 🙂

[@Alirazakb]

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[@VitalSine]

Thank you so much!

[@williewong2246]

1. Any survey papers on p-sum graphs? 2. Is there a recurrence relation to obtain p-sum graphs using (less-than-p)-sum graphs, say (p-1)-sum graphs, (p-2)-sum graphs,...?

[@VitalSine]

1. I do not know of a survey paper on the p-sum of graphs, but Dragos Cvetkovic has published several papers about the p-sum that you may find interesting: www.jstor.org/stable/43667432 www.jstor.org/stable/43667405 www.jstor.org/stable/43667429 2. I do not know of a recurrence relation for p-sum graphs such as you describe, but it's a really interesting question! I'll look into it and let you know if I can find anything about a recurrence relation.

[@TecoMix]

In the 2-sum of (G_1,G_2,G_3), b2** has more adjacencies, for example with b1*.