Let T be a regular map of type {p, q} on the torus, and let v, e,f be the numbers of its vertices, edges and faces, respectively From the iden- tities q • v = 2e = p- f
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[PDF] Math 228: Embedding graphs in surfaces - CMU Math
We now consider the question of vertices, edges, and faces drawn of K3,3 drawn on the torus Recall that we have the following theorem for plane graphs:
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(The Euler characteristic of the torus ) Suppose that G is a toroidal graph, and that G has V vertices, E edges and F faces Then V − E + F =
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Abstract Covering a toroidal surface by quadrilaterals and their transformation by leapfrog vertices, number of edges, number of faces, and genus) is obeyed
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Let T be a regular map of type {p, q} on the torus, and let v, e,f be the numbers of its vertices, edges and faces, respectively From the iden- tities q • v = 2e = p- f
[PDF] GRAPHS, KNOTS AND SURFACES - School of Mathematics and
Similarly, the torus defined later is a model of the surface of a doughnut The number of vertices, edges and faces may be increased at will by subdivision
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a minimal forbidden subgraph for the torus by the edge-by-edge elimination) The face-width fw(G,Π) of a nonplanar embedding Π of G is the minimum integer k such that vertices but no internal vertex on this path is a branch vertex
Irreducible Quadrangulations of the Torus - ScienceDirect
Let G be a quadrangulation of a closed surface F2 and f a face of G with its boundary the projective plane, identify each antipodal pair of vertices and edges of
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2 Page 3 are the faces of G G∗ is constructed by placing a new vertex in each face of G, and joining two new face-vertices by an edge whenever the
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This is suffcient to determine the faces (2-cells) of the embedding If G has n vertices, ε edges, and f faces, then Euler's formula tells us that in a 2-cell embedding,
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