The composition ![G=G_1[G_2]](/images/equations/GraphComposition/Inline1.svg)
of graphs 
and 
with disjoint point sets 
and 
and edge sets 
and 
is the graph with point vertex 
and 
adjacent with 
whenever ![[u_1 adj v_1]](/images/equations/GraphComposition/Inline11.svg)
or ![[u_1=v_1 and u_2 adj v_2]](/images/equations/GraphComposition/Inline12.svg)
(Harary 1994, p. 22). It is also
called the graph lexicographic product.
Graph Composition
See also
Graph Lexicographic Product, Graph ProductExplore with Wolfram|Alpha
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 Web Resource. https://mathworld.wolfram.com/GraphComposition.html