4 edition of **Locally finite, planar, edge-transitive graphs** found in the catalog.

- 313 Want to read
- 18 Currently reading

Published
**1997**
by American Mathematical Society in Providence, R.I
.

Written in English

- Paths and cycles (Graph theory),
- Group theory.

**Edition Notes**

Statement | Jack E. Graver, Mark E. Watkins. |

Series | Memoirs of the American Mathematical Society,, no. 601 |

Contributions | Watkins, Mark E., 1937- |

Classifications | |
---|---|

LC Classifications | QA3 .A57 no. 601, QA166.22 .A57 no. 601 |

The Physical Object | |

Pagination | vi, 75 p. : |

Number of Pages | 75 |

ID Numbers | |

Open Library | OL998673M |

ISBN 10 | 0821805568 |

LC Control Number | 96037447 |

How can we find the proof of the following statement: An undirected graph is edge transitive if and only if its line graph is vertex transitive. Stack Exchange Network Stack Exchange network consists of Q&A communities including Stack Overflow, the largest, most trusted online community for developers to learn, share their knowledge, and. $\begingroup$ If you're asking for graphs that are vertex-transitive but not edge-transitive, the complement of any cycle with seven or more vertices will do. Or google Most vertex transitive graphs will not be edge transitive. $\endgroup$ – Chris Godsil Nov 26 '17 at

A classification is given for edge transitive circulant graphs whose complements are also edge transitive. In particular, it is shown that the only self-complementary symmetric circulant graphs are certain Paley graphs with a prime number of vertices. Similar results on digraphs are also by: 4. 1 Sebastian M. Cioabă, Jack H. Koolen, Hiroshi Nozaki, Jason R. Vermette, Maximizing the Order of a Regular Graph of Given Valency and Second Eigenvalue, SIAM Journal on Discrete Mathematics, , 30, 3, CrossRef; 2 Xiuyun Wang, Yanquan Feng, Jinxin Zhou, Jihui Wang, Qiaoling Ma, Tetravalent half-arc-transitive graphs of order a product of three primes, Discrete Mathematics, , , 5.

This in-depth coverage of important areas of graph theory maintains a focus on symmetry properties of graphs. Standard topics on graph automorphisms are presented early on, while in later chapters more specialised topics are tackled, such as graphical regular representations and by: Products of edge-transitive graphs with an interlude on the internet graph and an appendix on the cardinal product Wilfried Imrich Montanuniversit¨at Leoben, Austria Richard Hammack Virginia Commonwealth University, Richmond, Virginia, USA Sandi Klavˇzar University of Ljubljana, Slovenia TBI Winter Seminar , Bled, Slovenia February

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The nine finite, planar, 3-connected, edge-transitive graphs have been known and studied for many centuries. The infinite, locally finite, planar, 3-connected, edge-transitive graphs can be classified according to the number of their end.

The nine finite, planar, 3-connected, edge-transitive graphs have been known and studied for many centuries. The infinite, locally finite, planar, 3-connected, edge-transitive graphs can be classified according to the number of their ends (the supremum of the number of infinite components when a finite subgraph is deleted).

Destination page number Search scope Search Text Search scope Search Text. Get this from a library. Locally finite, planar, edge transitive graphs. [Jack E Graver; Mark E Watkins]. Our first major project was writing Combinatorics with Emphasis on the Theory of Graphs, #54 in the Springer Graduate Texts in Mathematics series ().

Twenty years and several papers later we wrote Locally Finite, Planar, Edge-transitive Graphs, # in Memoirs of the AMS. In the s, Wolfgang Jurkat and I published a series of papers on.

An approach to analysing the family of Cayley graphs for a finite group G is given which identifies normal edge-transitive Cayley graphs as a sub-family of central importance.

It is shown that the automorphism group of an infinite, locally finite, planar graph acts primitively on its vertex set if and only if the graph has connectivity 1 and, for some integer m⩾2, every vertex is incident with exactly m lobes, all of which are finite.

Specifically, edge-transitive graphs book all of the lobes are isomorphic to K 4 or all are circuits of length p for some odd prime by: 2. A complete presentation is given of the class g of locally finite, edge-transitive, 3-connected planar graphs. They are classified according to (1) the number of ends: zero (for the nine finite.

A tessellation is understood to be a 1-ended, locally finite, 3-connected planar map. The edge-symbol 〈p,q;k,ℓ〉 of an edge of a tessellation T is a 4-tuple listing the valences p and q of. He has published more than 60 research articles in combinatorics, particularly in algebraic and topological graph theory, and has coauthored (with J.E.

Graver) the graduate text Combinatorics with Emphasis on the Theory of Graphs ( Springer-Verlag, ) and Locally Finite, Planar, Edge-Transitive Graphs (MemoirAmer. Math. Soc 5/5(1). Section 6: the classification of locally finite, edge-transitive planar graphs by J.E. Graver and the author in terms of the number of ends, their Petrie walks, and the local behavior of their automorphism by: 4.

Edge-transitive graphs include any complete bipartite graph, and any symmetric graph, such as the vertices and edges of the cube. Symmetric graphs are also vertex-transitive (if they are connected), but in general edge-transitive graphs need not be vertex-transitive. The Gray graph is an example of a graph which is edge-transitive but not vertex-transitive.

A book review of the Open University’s course “Graphs, Networks, and Designs” ENVIRONMENT AND PLANNING B, Vol. 9, No. 4,pp An alternative approach to the dimension theorem for inner products, THE AMERICAN MATHEMATICAL MONTHLY, Vol. 94. Finite vertex-transitive graphs include the symmetric graphs (such as the Petersen graph, the Heawood graph and the vertices and edges of the Platonic solids).The finite Cayley graphs (such as cube-connected cycles) are also vertex-transitive, as are the vertices and edges of the Archimedean solids (though only two of these are symmetric).

Potočnik, Spiga and Verret have constructed a census. A map on a closed surface is a two-cell embedding of a finite connected graph. Maps on surfaces are conveniently described by certain trivalent graphs, known as flag graphs.

Flag graphs themselves may be considered as maps embedded in the same surface as the original graph. The flag graph is the underlying graph of the dual of the barycentric subdivision of the original : Tomaz Pisanski, Gordon I.

Williams, Leah Wrenn Berman. He has published more than 60 research articles in combinatorics, particularly in algebraic and topological graph theory, and has coauthored (with J.E.

Graver) the graduate text Combinatorics with Emphasis on the Theory of Graphs ( Springer-Verlag, ) and Locally Finite, Planar, Edge-Transitive Graphs (MemoirAmer.

Math. Soc. Locally finite, planar, edge-transitive graphs - Jack E. Graver and Mark E. Watkins: MEMO/ Gauge theory on compact surfaces - Ambar Sengupta: Volume Number Title; MEMO/ Large time behavior of solutions for general quasilinear hyperbolic-parabolic systems of conservation laws - Tai-Ping Liu and Yanni Zeng: MEMO/ The polycirculant conjecture asserts that every vertex-transitive digraph has a semiregular automorphism: a non-trivial automorphism whose cycles all have the same length.

In this paper, we investigate the existence of semiregular automorphisms of edge-transitive graphs. In particular, we show that any regular edge-transitive graph of valency three or four has a semiregular by: 3.

Combinatorics with Emphasis on the Theory of Graphs. Springer-Verlag New York. Jack E. Graver, Mark E.

Watkins Locally Finite, Planar, Edge-Transitive Graphs. Amer Mathematical Society. Jack E. Graver, Mark E. Watkins. A search query can be a title of the book, a. Our theory is built on analysing several special classes of Cayley graphs (de-ﬁned in Subsection), and analysing some operations on general Cayley graphs (discussed in Subsection).

Basic edge-transitive Cayley graphs. For two groups X and Y,denote by X Y a semidirect product of X by Y,andbyX Y the central product of X and Y. Abstract. In this chapter, based mainly on [], we focus on generalization of zigzags for higher ed by Coxeter’s notion of Petrie polygon for \(d\)-polytopes (see []), we generalize the notion of zigzag circuits on complexes and compute the zigzag structure for several interesting families of \(d\)-polytopes, including semiregular, regular-faced, Wythoff Archimedean ones.However, it still seems quite difficult to give a nice characterization of general edge-transitive dihedrants.

A Cayley graph Γ = Cay (G, S) is called X-normal edge-transitive, if X ≤ Aut Γ is transitive on E Γ and G is normal in X. Normal edge-transitive Cayley graphs were initiated by Praeger and have some nice properties; see.Cited by: 2.Abstract: We develop a new framework for analysing finite connected, oriented graphs of valency 4, which admit a vertex-transitive and edge-transitive group of automorphisms preserving the edge orientation.

We identify a sub-family of "basic" graphs such that each graph of this type is a normal cover of at least one basic graph.

The basic graphs either admit an edge-transitive group of.