✦ LIBER ✦

Constructing a Class of Symmetric Graphs

✍ Scribed by Sanming Zhou

Publisher: Elsevier Science
Year: 2002
Tongue: English
Weight: 208 KB
Volume: 23
Category: Article
ISSN: 0195-6698
DOI: 10.1006/eujc.2002.0600

No coin nor oath required. For personal study only.

✦ Synopsis

We find a natural construction of a large class of symmetric graphs from point-and block-transitive 1-designs. The graphs in this class can be characterized as G-symmetric graphs whose vertex sets admit a G-invariant partition B of block size at least 3 such that, for any two blocks B, C of B, either there is no edge between B and C, or there exists only one vertex in B not adjacent to any vertex in C. The special case where the quotient graph B of relative to B is a complete graph occurs if and only if the 1-design needed in the construction is a G-doubly transitive and G-block-transitive 2design, and in this case we give an explicit classification of when G is a doubly transitive projective group or an affine group containing the affine general group. Examples of such graphs include cross ratio graphs studied recently by Gardiner, Praeger and Zhou and some other graphs with vertices the (point, line)-flags of the projective or affine geometry.

📜 SIMILAR VOLUMES

A class of symmetric graphs with 2-arc t

A class of symmetric graphs with 2-arc transitive quotients

✍ Bin Jia; Zai Ping Lu; Gai Xia Wang 📂 Article 📅 2010 🏛 John Wiley and Sons 🌐 English ⚖ 179 KB

Let be an X -symmetric graph admitting an X -invariant partition B on V ( ) such that B is connected and (X , 2)-arc transitive. A characterization of ( , X , B) was given in [S. Zhou Eur J Comb 23 (2002), 741-760] for the case where |B|>| (C)∩B| = 2 for an arc (B, C) of B . We consider in this arti

N-extendability of symmetric graphs

✍ R. E. L. Aldred; D. A. Holton; Dingjun Lou 📂 Article 📅 1993 🏛 John Wiley and Sons 🌐 English ⚖ 361 KB

## Abstract It is proved that a cyclically (__k__ − 1)(2__n__ − 1)‐edge‐connected edge transitive __k__‐regular graph with even order is __n__‐extendable, where __k__ ≥ 3 and __k__ − 1 ≥ __n__ ≥ ⌈(__k__ + 1)/2⌉. The bound of cyclic edge connectivity is sharp when __k__ = 3. © 1993 John Wiley & Sons

A class of upper-embeddable graphs

✍ F. Jaeger; C. Payan; N. H. Xuong 📂 Article 📅 1979 🏛 John Wiley and Sons 🌐 English ⚖ 202 KB

## Abstract In this paper, we prove the following result: Every graph obtained by connecting (with any number of edges) two vertex‐disjoint upper‐embeddable graphs graphs with even Betti number is upper‐embeddable.

A class of Hamiltonian regular graphs

✍ Paul Erdös; Arthur M. Hobbs 📂 Article 📅 1978 🏛 John Wiley and Sons 🌐 English ⚖ 317 KB

## Abstract In this paper, we show that __n__ ⩾ 4 and if __G__ is a 2‐connected graph with 2__n__ or 2__n__−1 vertices which is regular of degree __n__−2, then __G__ is Hamiltonian if and only if __G__ is not the Petersen graph.

-constructibility of planar graphs

✍ C. M. Mynhardt; I. Broere 📂 Article 📅 1980 🏛 John Wiley and Sons 🌐 English ⚖ 386 KB

## Abstract In this paper, the concept of the 𝒢‐constructibility of graphs is introduced and investigated with particular reference to planar graphs. It is conjectured that the planar graphs are minimally __N__‐constructible, where __N__ is a finite set of graphs and an infinite set 𝒢 is obtained s

On 4-Valent Symmetric Graphs

✍ A. Gardiner; Cheryl E. Praeger 📂 Article 📅 1994 🏛 Elsevier Science 🌐 English ⚖ 261 KB

Let \(G\) act transitively on incident vertex, edge pairs of the connected 4-valent graph \(\Gamma\). If a normal subgroup \(N\) does not give rise to a natural 4-valent quotient \(\Gamma_{N}\) with \(G / N\) acting transitively on incident vertex, edge pairs, then either (a) \(N\) has just one or t