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The concept of a graph algebra was introduced by G.F. McNulty and C.R. Shallon in 1983. Let <math>D=(V,E)</math> be a directed graph (see [[Graph (data structure)]]), and let <math>0</math> be an element not in <math>V</math>. The ''graph algebra'' associated with <math>D</math> is the set <math>V \cup \{0\}</math> equipped with multiplication defined by the rules <math>xy = x</math> if <math>x,y\in V,(x,y)\in E</math>, and <math>xy = 0</math> if <math>x,y\in V\cup \{0\},(x,y)\notin E</math>.
Graph algebras have been used in several directions of mathematics and computer science in constructions concerning, for example, dualities, equational theories ([[equational theory]]), varieties ([[variety (universal algebra)]]), [[finite state automata]] or [[finite state machines]], etc.
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