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Showing 1 to 5 of 5 for “"Category of Graphs"”.
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Topos-like Properties in Two Categories of Graphs and Graph-like Features in an Abstract Category
In the study of the Category of Graphs, the usual notion of a graph is that of a simple graph with at most one loop on any vertex, and the usual notion of a graph homomorphism is a mapping of graphs that sends vertices to vertices, edges to edges, and preserves incidence of the mapped vertices and …
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Topos-like Properties in Two Categories of Graphs and Graph-like Features in an Abstract Category
In the study of the Category of Graphs, the usual notion of a graph is that of a simple graph with at most one loop on any vertex, and the usual notion of a graph homomorphism is a mapping of graphs that sends vertices to vertices, edges to edges, and preserves incidence of the mapped vertices and …
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The Hanna Neumann conjecture: A flow detection approach
… Neumann Conjecture states that if two subgroups of a finitely generated free group have finite ranks m and n, then their intersection has rank N which satisfies $N$ $-$ 1 $\leq$ ($m$ $-$ 1)($n$ $-$ 1). The current work examines this conjecture by restating it in terms of a stronger conjecture on …
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The Categories of Graphs
<p>In traditional studies of graph theory, the graphs allow only one edge to be incident to any two vertices, not necessarily distinct, and the graph morphisms must map edges to edges and vertices to vertices while preserving incidence. We refer to these restricted morphisms as <i>strict …
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The Categories of Graphs
<p>In traditional studies of graph theory, the graphs allow only one edge to be incident to any two vertices, not necessarily distinct, and the graph morphisms must map edges to edges and vertices to vertices while preserving incidence. We refer to these restricted morphisms as <i>strict …