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Questions about the branch of combinatorics called graph theory (not to be used for questions concerning the graph of a function). This tag can be further specialized via using it in combination with more specialized tags such as extremal-graph-theory, spectral-graph-theory, algebraic-graph-theory, topological-graph-theory, random-graphs, graph-colorings and several others.

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Algebraic structure generated by primitive graph operations

Perhaps this paper might be tangentially related to the ideas you are developing? Bilal Khan, Kiran Bhutani, Delaram Kahrobaei. A Graphic Generalization of Arithmetic, Electronic Journal of Combinato …