J. L. Gross and T. W. Tucker, Topological Graph Theory. New York: John Wiley and Sons, 1987.  Home/Search   Document Not in Database   Summary   Related Articles   Check

....with each vertex; the latter is called a local rotation. Basically, the local rotations records the cyclic order of the edges at a vertex, while the signature is used to keep track of whether that order is in a local clockwise or local anticlockwise sense. For more details we refer the reader to [4]. When studying projective planar embeddings it is common to x the signature on the graph. A projective planar embedding of such a signed graph then has the property that a cycle is unbalanced if and only if it is essential. In this paper we will give a characterization of which signed graphs ....

J.L. Gross and T. Tucker, "Topological Graph Theory", Wiley, New York (1987).

....span radical hyperplanes that intersect in a single (d 3) at, called the radical centre . A nite simplicial k complex C(S) with S = Y j is a connected or unconnected collection of simplexes (or: simplices) with 0 k d and ( 1) all satisfying two properties ( 20] 14] 21] [15]) 2 C ) C 2 C; C C = C C = C (16) Apparently, every sub face of a simplex needs to be in C too, and every sub complex C C. A simplicial complex may degenerate to a point set, a linear graph, etc. having some ....

....E ) nding expressions for the number of k faces is not trivial. However, a fully triangulated single d skeleton serves as an upper bound: with 1) O(C ) O(T ) where T is a triangulation of point set S. Refer to Edelsbrunner, 10] 12] Del nado and Edelsbrunner, 7] Gross and Tucker, [15]. Weights can be generated on a per point basis, they can also be generated as a function f : E R. Weights are called unstructured weights if two arbitrary functions values (function images) f(x 1 ) and f(x 2 ) x 1 ; x 2 2 E have auto covariance cov xx (x 1 ; x 2 ) 0. 24 ....

Jonathan L. Gross and Thomas W. Tucker. Topological Graph Theory. John Wiley & Sons, New York, 1987. 25

....the Four Color Problem see [6] and [16] Biggs, Lloyd, and Wilson [4] give an excellent history of the rst 200 years of graph theory, including its topological origins. There are several in depth books for the researcher in the area. We mention in particular those of White [18] Gross and Tucker [7], and Mohar and Thomassen [11] For the reader seeking more background, we recommend the introductory graph theory text by West [17] For an on going list of open problems in topological graph theory we refer the reader to hhttp: www.emba.uvm.edu archdeac problems i. Some open problems about ....

J. Gross and T. Tucker, Topological graph theory, John Wiley and Sons, New York (1987).

....deg(v) Though multigraphs do occur in this paper, all the cases that have to be discussed in detail deal with simple graphs, so we adapted our notation to them. All graphs are assumed to be connected and all embedded graphs to be embedded in the plane, described by a rotation system like e.g. in [13] or [20] So we can represent every edge by two directed edges inverse to each other (we write e 1 for the inverse of edge e) and every vertex v comes with a cyclic ordering of the edges starting at v, which we interpret as clockwise. An isomorphism of an embedded graph is a graph theoretic ....

J.L. Gross and T.W. Tucker. Topological Graph Theory. John Wiley and Sons, 1987.

....edges) of G and, f preserves the adjacency between vertices and edges: if v 2 V (H) is adjacent to e 2 E(H) then f(v) 2 V (G) is adjacent to f(e) 2 E(G) Let us recall that a vertex v 2 V (G) is said to be adjacent to an edge e 2 E(G) if v 2 e. The most popular graph maps are coverings [7]. A graph map f : H G is a covering if both H and G are connected and for each vertex v 2 V (H) the map f maps bijectively the edges adjacent to v in H to the edges adjacent to f(v) 2 V (G) In Computer Science graph coverings were used to show some impossibility results in distributed ....

J.L. Gross and T.W. Tucker. Topological Graph Theory. John Wiley & Sons, 1987.

....new in the study of topological modeling. The graph rotation system is a powerful tool for guaranteeing topological consistency and provides great convenience in topology changes. In this section, we introduce historical background and some mathematical fundamentals for graph rotation systems (see [18] for more detailed discussion) The concept of rotation systems of a graph originated from the study of graph embeddings and it is implicitly due to Heffter [21] who used it in Poincare dual form. A graph embedding in an orientable surface corresponds to an obvious rotation system, namely, the ....

....approach can also be extended to include topological changes into progressive meshes [24] and multiresolution representations of meshes [13, 9] Two major operations in progressive meshes technique are vertex split and edge collapse. It can be shown that these operations do not change the topology [18]. The same can also be easily shown for multiresolution representations of meshes. In fact, one of the major problem in multiresolution mesh morphing is that source and target must share the same topology [25] By including the edge insertion and edge deletion operations, it is possible to change ....

J. L. Gross and T. W. Tucker, Topological Graph Theory, (Wiley Interscience, New York, 1987).

....with deep algebraic questions related to groups acting on trees (Bass and Kulkarni [4] Graph coverings are naturally related to subgroups of free groups; see Stillwell [14] and Stallings [13] for example. Finally, as purely graph theoretic objects, they were studied by Gross and Tucker [7] [8], Negami [12] and Archdeacon and Richter [3] among others. The main theme of this work is the introduction of a probabilistic structure on the set of graphs that cover a xed base graph. This enables one to apply the powerful probabilistic method to questions concerning coverings. We may ....

J. L. Gross and T. W. Tucker. Topological Graph Theory. WileyInterscience, 1987. 19

....for subsets V . A switching class is an equivalence class of graphs under switching, see the survey papers by Seidel [11] and Seidel and Taylor [12] Generalizations of this approach where the graphs are labelled with elements of a group other than Z 2 can be found in Gross and Tucker [6], Zaslavsky [13] the book of Ehrenfeucht, Harju and Rozenberg [5] and the thesis of Hage [7] A property P of graphs can be transformed into an existential property of switching classes as follows: P (G) if and only if there is a graph H [G] such that P(H) We will also refer to P as ....

J.L. Gross and T.W. Tucker. Topological Graph Theory. Wiley, New York, 1987.

....random structures. This enables us to improve (slightly) the known bounds for the edge expansion of regular graphs. 1 Introduction In [4] we introduced a simple model for a random nite covering G G of a xed base graph G (Here covering is in the topological sense of covering maps, as in [7] and [9] We recall the construction. Given a connected graph G and a natural number n (the order of the covering) we orient the edges of G arbitrarily and assign a permutation e 2 S n to each edge e 2 E(G) using some probability distribution over S n (usually, we use the uniform ....

J. L. Gross and T. W. Tucker. Topological Graph Theory. WileyInterscience, 1987.

....set of darts of M , that is, the stabilizer in Aut(M) of each arc of M is trivial. If the action of Aut(M) on the darts of M is transitive (and therefore regular) we say that the Cayley map M is a regular Cayley map. The reader interested in more information on regular maps is advised to consult [3], 1] or [9] 3 Skew morphisms of nite groups We will take particular advantage of a necessary and sucient condition for a Cayley map M to be regular, based on the concept of a skew morphism introduced in [4] Let H be a nite group, H H a permutation of H of order k (in the full ....

J.L.Gross and T.W. Tucker, Topological graph theory, Wiley, New York, 1987.

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J. L. Gross and T. W. Tucker, Topological Graph Theory. New York: John Wiley and Sons, 1987.

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J. L. Gross and T. W. Tucker. Topological Graph Theory. John Wiley and Sons, New York, 1987.

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Gross, Jonathan L., and Tucker, T. W., 1987, Topological Graph Theory, Wiley-Interscience, New York.

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J. Gross and T. Tucker, Topological Graph Theory, Wiley, New York (1987).

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Jonathan Gross and Thomas Tucker, Topological Graph Theory , John Wiley and Sons, New York, 1987.

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Gross, J. L., and Tucker, T. W. Topological Graph Theory. J. Wiley and Sons, 1987.

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J. L. Gross and T. W. Tucker, Topological Graph Theory, Wiley-Interscience, New York, 1987.

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J.L. Gross and T.W. Tucker, Topological Graph Theory, John Wiley & Sons, New York, 1987.

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Jonathan L. Gross and Thomas W. Tucker. Topological Graph Theory. J. Wiley and Sons, 1987.

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J.L. Gross and T.W. Tucker, Topological Graph Theory, John Wiley & Sons, New York, 1987.

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J. L. Gross and T. W. Tucker, Topological Graph Theory, Wiley-Interscience, New York, 1987.

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J. L. Gross and T. W. Tucker. Topological Graph Theory. Wiley, New York, 1987.

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Jonathan L. Gross and Thomas W. Tucker. Topological Graph Theory. J. Wiley and Sons, 1987.

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J.L.Gross et al., "Topological Graph Theory", John Wiley&Sons, Inc. 1987.

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Jonathan Gross and Thomas Tucker, Topological Graph Theory, Wiley, New York (1987)

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