Vector Spaces and Kirchhoff Graphs

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This project concerns chemical, electrochemical, and biochemical reaction networks, reaction routes (reaction pathways) through these networks, and the depiction of these networks using Kirchhoff graphs. This work will build on a vector space approach to reaction routes to establish that one or more Kirchhoff graphs exist for any given reaction network and to develop a method for constructing these graphs. Neither of these results is obvious for arbitrary reaction networks. Results of the project will significantly aid fundamental understanding of reaction networks and have potential application to the design of fuel cells and other devices involving complicated chemical reaction networks.