Talk:Tensor product of graphs


 * The double cover of a complete graph is a complete bipartite graph: K2 × Kn = Kn,n.

This is not true. For example, take n to be 3. K2 × K3 = C6.

—Preceding unsigned comment added by BorisHorvat (talk • contribs)


 * It's the complete graph minus a matching. I took out that line. —David Eppstein 17:11, 12 February 2007 (UTC)

K2 × G is called the bipartite double of G in many graph theory textbooks. Wpolly (talk) 17:09, 24 January 2009 (UTC)
 * For a general graph G, there usually are other double covers possible (For instance, the Icosahedral Graph is a double cover of K6).


 * I tried to clarify the terminology related to double covers and bipartite double covers a bit. Some references would be nice; it is easy to find journal articles that use these terms, but if someone has suitable textbooks at hand, please add citations. —Preceding unsigned comment added by Miym (talk • contribs) 18:20, 24 January 2009 (UTC)


 * I added a little more including a reference specifically about bipartite double covers (not the same as textbook coverage but still better than no reference). —David Eppstein (talk) 22:22, 24 January 2009 (UTC)


 * I tried to clarify the concept of a bipartite double cover with some illustrations. I also tried to make a distinction between covering in graph theory and covering in topology (I think we should give a self-contained graph-theoretic definition of a covering graph without referring to Covering space). But if you do not like it, feel free to revert the changes. It is also possible that I made some mistakes with the quick'n'dirty examples; please check them if you have time. — Miym (talk) 01:37, 25 January 2009 (UTC)


 * This material was starting to overload the article. I moved it to a separate article, bipartite double cover. —David Eppstein (talk) 02:08, 25 January 2009 (UTC)


 * Looks great! Thanks! — Miym (talk) 10:30, 25 January 2009 (UTC)


 * Now there is an article about covering graphs. — Miym (talk) 14:08, 25 January 2009 (UTC)

Support for "tensor product" as main name?
The references cited here use a variety of different terms for this product, but none of them uses the term "tensor product". Is there a credible source that indicates why "tensor product" should be the main term, when "direct product" is the term preferred by the standard reference textbook (Imrich and Klavzar p.162), Russell and Whitehead do not actually name their products (and certainly not on page II.384), both the MathWorld article and Hahn & Sabidussi prefer categorical product, and Weichsel unusually uses Kronecker product? Older work by Imrich (e.g. with Pultr in 1991) uses "tensor product", but in more recent papers he seems to have switched to direct product.

Tensor is strongly associated with tensor product of matrices, which is a completely different concept. It can also be used to unify several of the graph products (see Imrich/Klavzar p.277 and 283). It would therefore seem a good idea to avoid "tensor product" as the primary name. I contend that the Wikipedia name for a concept tends to endorse a particular nomenclature, and if Wikipedia is supporting a particular nomenclature, then it must provide some citations in support. Right now the citations are supporting "direct" or "categorical".

Unless someone can add credible references using "tensor product", either direct product or categorical product would be preferable names, and I suggest renaming this page in accordance. The name tensor product would then be relegated to a historical curiosity.

Ott2 (talk) 17:10, 20 October 2012 (UTC)
 * Google scholar has about 126 hits for the phrase "tensor product of graphs". In comparison, it has only about 91 for "categorical product of graphs", about 183 for "kronecker product of graphs", and about 202 for "direct product of graphs". So all four of these seem to be in similarly common usage. —David Eppstein (talk) 17:40, 20 October 2012 (UTC)