Definition talk:Graph (Graph Theory)

In the Definition category, this shows up under D instead of G... Why is this and how do I fix it?

Thanks, -Dan

Never mind, I figured it out. -Dan

Refactor
Large but probably valuable project: turn this into a disambiguation page covering simple graphs, loop graphs, digraphs, loop digraphs, multigraphs, multidigraphs, pseudographs, pseudodigraphs, etc. A number of pages already seem to use this one as though it were something other than what it is. Vertices in Locally Finite Graph is clearly talking about some sort of multigraph/pseudograph, but just points here. Said theorem holds for simple graphs in such a trivial fashion as not to be worth mentioning, but as can be seen there it requires more work in other cases. --Dfeuer (talk) 19:44, 30 May 2013 (UTC)


 * Bad idea. --prime mover (talk) 20:08, 30 May 2013 (UTC)


 * Regardless of the possible merit such a page could have, I deem the graph theory section insufficiently populated to make this worthwhile presently. But we can keep the suggestion for later times. &mdash; Lord_Farin (talk) 21:44, 30 May 2013 (UTC)


 * As a graph theorist, I support this in principle. Maybe on one bored night I'll go through and actually go and refactor it and then try to cover some more basic results, as I did a long time ago. I recall a discussion about the best way to define a graph. Based on my work in algebra on graphs, the most general way is to define an edge set $E$, a vertex set $V$, an incidence relation on $V \times E$, and some way of labeling vertices, edges, and tentacles (a tentacle is a vertex-edge pair). Digraphs can be expressed via labeling tentacles.


 * My suggestion would be to attempt to present the most general definition possible, and then provide all the useful special cases. For instance, a simple undirected graph can be expressed as $\left(V, E\right)$ where $E \subseteq V$ and every edge has size 2. In this case, the incidence relation simply is $\in$. Every result should be as general as possible, perhaps with useful special cases mentioned where it's practical. As a perhaps-useful comparison, one of the most powerful results of the Graph Minors Project, of which the Graph Minor Theorem is a special case, is an expression about labeled hypgraphs. Scshunt (talk) 09:05, 5 August 2014 (UTC)