Graph Tensor Product
The graph tensor product, also called the graph cardinal product (Imrich 1998), graph categorical product, graph conjunction, graph direct product (Hammack et al. 2016), graph Kronecker product (Weichsel 1962), graph relational product, or graph weak direct product, is the graph product denoted G×H and defined by the adjacency relations (gadjg^' and hadjh^').
Letting A(G) denote the adjacency matrix, the graph tensor product of simple graphs G and H is given by
| A(G×H)=A(G) tensor A(H), |
where tensor denotes the Kronecker product (Hammack et al. 2016).
The graph tensor product G×K_2 is known as the bipartite double graph of G.
See also
Bipartite Double Graph, Double Graph, Graph ProductPortions of this entry contributed by Nicolas Bray
Portions of this entry contributed by Lorenzo Sauras-Altuzarra
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References
Hammack, R.; Imrich, W.; and Klavžar, S. Handbook of Product Graphs, 2nd ed. Boca Raton, FL: CRC Press, 2016.Imrich, W.; Klavzar, S.; and Rall, D. F. Graphs and their Cartesian Product. Wellesley, MA: A K Peters, 2008.Imrich, W. "Factoring Cardinal Product Graphs in Polynomial Time." Disc. Math. 192, 119-144, 1998.Weichsel, P. M. "The Kronecker Product of Graphs." Proc. Amer. Math. Soc. 13, 47-52, 1962.Referenced on Wolfram|Alpha
Graph Tensor ProductCite this as:
Bray, Nicolas; Sauras-Altuzarra, Lorenzo; and Weisstein, Eric W. "Graph Tensor Product." From MathWorld--A Wolfram Resource. https://mathworld.wolfram.com/GraphTensorProduct.html