Boyle has given a condition for defining a homomorphism in terms of minimal paths for undirected graphs. The purpose of such homomorphisms is to provide a simpler graph which will reflect the structure of the more complex graph, and thereby enable the researcher to make observations which may have been shrouded by a preponderance of nodes and edges. This paper develops Boyle's ideas and introduces further homomorphisms for directed as well as undirected graphs. The relationships between the various homomorphisms are also examined.
Partitions and homomorphisms in directed and undirected graphs
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