I would even say that "Everyone Should Start Doing Graph Theory", but it's only my opinion of course. Take it or leave it.
I remember to this day the exact location I was when being introduced to construct hypercubes, to the exact bench in our uni cafeteria. It changed my understanding of multidimensionality completely.
Graphs in general are high dimensional structures and don't lend themselves to 2D projections. That is not a problem with coding the layouting algorithm. There simply is no good geometric arrangement for most graphs / networks because they are not planar [0], or even close to it (with few intersections).
Related HN thread: https://news.ycombinator.com/item?id=17745779
AHH. Definition 1.4 and the questions after did it. It went from "Tracking all" to "I don't understand how this follows at all, and this makes no sense to me" 1.3b is a graph, not a union of two graphs?. What are the "two graphs"? What is this operator-like algebra, and what does it have to do with the rest of the definition or the text before and after it? A question about the complement which was never defined? Why are we probably agreeing that {1, 2} contain 3?
Update: Better phrasing I can understand:
"Definition 1.4. The union of two graphs G and H, denoted <>, is a single graph containing all vertices and edges from both. If G and H share no vertices in common, <> is a disjoint union."
For 1.5, I had no idea what the written definition meant, but this does: ``` Definition 1.5. The complement of graph G is the one that has the same vertices, two vertices are connected in G_complement if and only if they are not connected in G.
There are plenty of ways to get a copy.
(Edit) But I understand that goal of a book can be completely different. So it's just problem of my expectations.
Yes, but I think it's important to state that it's only reliable for things that are very well known and extensively written about.
And for the bleeding edge part: My godchild wanted to know the name of a Pokémon from his licensed shirt. One of the first ones, found in every training set. Couldn't get it right, was certain it was the wrong one.
how did you even ask an AI this question? Took a picture of the shirt, uploaded it, and asked the AI what it was? That's a different class of problem than "answer this graph theory question and include your references: <paste text here>"
You don't ask for proofs to print them out, put them in your drawer, and brag around that you own the proofs for these exercises.
You ask Claude for proofs to help your understanding. Understanding is the exact same activity as verifying.
(Assuming it's a proof or something - if it's just a number - oh well).