{
  "id": "1612.00601",
  "version": "v1",
  "published": "2016-12-02T09:04:54.000Z",
  "updated": "2016-12-02T09:04:54.000Z",
  "title": "Products and tensor products of graphs and homomorphisms",
  "authors": [
    "Izak Broere",
    "Johannes Heidema"
  ],
  "comment": "Comments: 12 pages; Subjects: Combinatorics (math.CO); Discrete Mathematics (cs.DM)",
  "categories": [
    "math.CO"
  ],
  "abstract": "We introduce and study, for a process P delivering edges on the Cartesian product of the vertex sets of a given set of graphs, the P-product of these graphs, thereby generalizing many types of product graph. Analogous to the notion of a multilinear map (from linear algebra), a P-morphism is introduced and utilised to define a P-tensor product of graphs, after which its uniqueness is demonstrated. Congruences of graphs are utilised to show a way to handle projections (being weak homomorphisms) in this context. Finally, the graph of a homomorphism and a P-tensor product of homomorphisms are introduced, studied, and linked to the P-tensor product of graphs.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2016-12-02T09:04:54.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "05C76",
      "05C25"
    ],
    "keywords": [
      "tensor products",
      "p-tensor product",
      "linear algebra",
      "weak homomorphisms",
      "handle projections"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 12,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}