Graph Composition
GraphCompositions
The composition G=G_1[G_2] of graphs G_1 and G_2 with disjoint point sets V_1 and V_2 and edge sets X_1 and X_2 is the graph with point vertex V_1×V_2 and u=(u_1,u_2) adjacent with v=(v_1,v_2) whenever [u_1 adj v_1] or [u_1=v_1 and u_2 adj v_2] (Harary 1994, p. 22). It is also called the graph lexicographic product.
See also
Graph Lexicographic Product, Graph ProductExplore with Wolfram|Alpha
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References
Harary, F. Graph Theory. Reading, MA: Addison-Wesley, p. 22, 1994.Imrich, W.; Klavzar, S.; and Rall, D. F. Graphs and their Cartesian Product. Wellesley, MA: A K Peters, 2008.Referenced on Wolfram|Alpha
Graph CompositionCite this as:
Weisstein, Eric W. "Graph Composition." From MathWorld--A Wolfram Resource. https://mathworld.wolfram.com/GraphComposition.html