Talk:Graph property
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I do not think that redirecting graph invariant to graph property is a good idea. To me a graph invariant is a mathematical concept (usually a number) associated with a graph that stays the same (= is invariant) under the graph isomorphism. For instance, the sum of the elementes of the first row of the adjacency matrix is not a graph invariant (since it depends on the vertex ordering) while the maximal row sum (= maximal degree of the graph) is a graph invariant.Tomo (talk) 06:29, 7 August 2008 (UTC)
Invariant discussion edit
I find the current writeup of graph invariants to be poorly written. A property is said to be a "descriptive characterization of [a] graph." Lets assume for the moment this does no allow qualitative characterizations. The article then defines a graph invariant as "an indexed family of graph properties." This is confusing when one rereads the given example of a graph property ("graph does not have vertices of degree 1").
The given example does not help. Indeed, I think it's wrong:
For example "the number of vertices" is an indexed family of graph properties "a graph has M edges, M = 0, 1, 2....".
Shouldn't that read:
For example "the number of vertices" is an indexed family of graph properties "a graph has N vertices, N = 0, 1, 2....".
Or have I misunderstood? Pugget (talk) 19:05, 22 March 2009 (UTC)
"monotone property" edit
Please see my edits at Hereditary property regarding the meaning of "monotone property". Actually I'm not sure that "hereditary" is any more uniquely defined but I'm out of steam for now. Someone else feel free... McKay (talk) 11:47, 23 March 2009 (UTC)
Lead paragraph edit
I don't think readers will understand "inherently graph-theoretical". It sounds like a contrast with inherently topological (e.g. the graph genus) or inherently linear algebraic (e.g. the eigenvalues). I suggest: