The definitions of a homomorphism and a contraction of a graph are generalized to digraphs. Solutions are given to the graph equation <mml:math alttext="$\overline {\phi \left( D \right)}  = \theta _\phi  \left( {\bar D} \right)$" xmlns:mml="http://www.w3.org/1998/Math/MathML"><mml:mrow><mml:mover accent="true"><mml:mrow><mml:mi>&#981;</mml:mi><mml:mrow><mml:mo>(</mml:mo><mml:mi>D</mml:mi><mml:mo>)</mml:mo></mml:mrow></mml:mrow><mml:mo stretchy="true">&#175;</mml:mo></mml:mover><mml:mo>=</mml:mo><mml:msub><mml:mi>&#952;</mml:mi><mml:mi>&#981;</mml:mi></mml:msub><mml:mrow><mml:mo>(</mml:mo><mml:mover accent="true"><mml:mi>D</mml:mi><mml:mo>&#175;</mml:mo></mml:mover><mml:mo>)</mml:mo></mml:mrow></mml:mrow></mml:math>.

International Journal of Mathematics and Mathematical Sciences

A digraph equation for homomorphic images

Abstract

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