Displaying similar documents to “An equivalence criterion for 3-manifolds.”

3-manifold spines and bijoins.

Luigi Grasselli (1990)

Revista Matemática de la Universidad Complutense de Madrid

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We describe a combinatorial algorithm for constructing all orientable 3-manifolds with a given standard bidimensional spine by making use of the idea of bijoin (Bandieri and Gagliardi (1982), Graselli (1985)) over a suitable pseudosimplicial triangulation of the spine.

On 3-simplicial vertices in planar graphs

Endre Boros, Robert E. Jamison, Renu Laskar, Henry Martyn Mulder (2004)

Discussiones Mathematicae Graph Theory

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A vertex v in a graph G = (V,E) is k-simplicial if the neighborhood N(v) of v can be vertex-covered by k or fewer complete graphs. The main result of the paper states that a planar graph of order at least four has at least four 3-simplicial vertices of degree at most five. This result is a strengthening of the classical corollary of Euler's Formula that a planar graph of order at least four contains at least four vertices of degree at most five.

Vertex-antimagic total labelings of graphs

Martin Bača, James A. MacDougall, François Bertault, Mirka Miller, Rinovia Simanjuntak, Slamin (2003)

Discussiones Mathematicae Graph Theory

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In this paper we introduce a new type of graph labeling for a graph G(V,E) called an (a,d)-vertex-antimagic total labeling. In this labeling we assign to the vertices and edges the consecutive integers from 1 to |V|+|E| and calculate the sum of labels at each vertex, i.e., the vertex label added to the labels on its incident edges. These sums form an arithmetical progression with initial term a and common difference d. We investigate basic properties of these labelings,...