Is the empty graph a pointless concept?

Have you taken a course in graph theory? It comes up in proofs where you need to do induction on the number of edges, for instance. By empty graph, I'm assume you mean: any number of vertices, and no edges.

>>7948407
It's meant by the graph on zero vertices, which is occasionally an annoyance as a base case.

Is zero a pointless concept?

Why would it be an annoyance? Can you mention any true statement that is difficult to prove for the empty graph?

>>7948451
it's rather when obviously true statements fail for the empty graph

I don't think that happens "occasionally", that the
empty graph becomes the base case for a proof
by induction of a statement that fails for it.

>>7948396
Yes. Start adding points and you'll have a concept.
>>7948434
Yes. If it had a point, it wouldn't be zero. Pointless concepts tend to be more useful than people tend to give them credit for.
>>7948479
Sounds like you need some null grounding, before you write another 20 or so security vulnerabilities.

>>7948524
Is posting with a name a pointless concept?

>>7948558
Yes, but it's not useless. That is, in a graph where namefagging is a single node, there are a nonzero number of connections to that node. Strictly so.

>>7948524
Lmao good luck forming the category of graphs without an initial object you stupid dumbass.

>>7948709
>the category of graphs
You don't need a category to do math. Do you even understand category theory?

>graph theory so diluted by computer scientist retards that they want to get rid of their empty object.

>empty graph
>pointless
I think this thread got posted because for the pun.

Anyway the main utility of the thing is to make the axioms cleaner. I'd rather have an empty graph than an empty graph-exclusion axiom.

>>7948700
Heres some more paper titles

>Hodge's general conjecture is false for trivial reasons
>You Could Have Invented Spectral Sequences
>Can one hear the shape of a drum?
>A minus sign that used to annoy me but now I know why it is there
>How not to prove the Poincare Conjecture
>Ramanujan's association with radicals in India
>Is the null-graph a pointless concept?
>Everybody knows what a Hopf algebra is
>On O_n
>Free rings and their relations
>Six standard deviations suffice.
>The importance of being straight
>The homotopy category is a homotopy category
>Division by three
>A Group of Order 8,315,553,613,086,720,000
>Holey Sheets
>On groups of order one.
>K-Theory and Reality
>The Joy of Sets.
>Applied Mathematics is Bad Mathematics
>Making the most out of zero branes and a weak background

more
http://www2.tcs.ifi.lmu.de/~jjohanns/cute.html

>MUH SHAPES N LINES N DOTS

Seriously fuck off

>>7948718
Lmao this is what undergrads think.

>>7948878
My point exactly.

>>7948451

Let [math]G[/math] be a simple undirected graph with [math]|V(G)|≥1[/math] alll day erryday

>>7948407
>By empty graph, I'm assume you mean: any number of vertices, and no edges.

That's the null graph, or [math]nK_1[/math].

>>7949743
I'm not that guy but there are lots of categories one might study that don't have these properties, anon.

>>7950487
>categories without initial objects
Lmao ok might as well just kill yourself

>>7950662
You should probably learn real category before making retarded claims like this.