Proposal: Graph generators for graphs defined by systems of equations
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Vladislav Taranchuk
Apr 28, 2026, 2:38:05 PM (3 days ago) Apr 28
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Hello,
I am proposing to add constructors for bipartite graphs whose adjacency relation is defined by a triangular system of equations over a finite commutative ring; see the recent survey of Lazebnik and Wang:
Besides explicit graph-returning constructors, the implementation has a descriptor object which validates and stores the defining equations. This lets users study the properties of the corresponding graph without constructing the full graph, which can be useful in extremal graph theory computations.
In a first iteration, I plan to include several standard families from the literature, including Wenger graphs, D(k, q) graphs, and A(k, q) graphs.
I already have a working prototype. Does this seem appropriate for Sage’s graph theory library, and in particular for `sage.graphs.generators`?
I am proposing to add constructors for bipartite graphs whose adjacency relation is defined by a triangular system of equations over a finite commutative ring; see the recent survey of Lazebnik and Wang:
Besides explicit graph-returning constructors, the implementation has a descriptor object which validates and stores the defining equations. This lets users study the properties of the corresponding graph without constructing the full graph, which can be useful in extremal graph theory computations.
In a first iteration, I plan to include several standard families from the literature, including Wenger graphs, D(k, q) graphs, and A(k, q) graphs.
I already have a working prototype. Does this seem appropriate for Sage’s graph theory library, and in particular for `sage.graphs.generators`?
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