By Jack Koolen, Jin Ho Kwak, Ming-Yao Xu

ISBN-10: 0415471842

ISBN-13: 9780415471848

**Applications of workforce thought to Combinatorics** comprises eleven survey papers from overseas specialists in combinatorics, staff thought and combinatorial topology. The contributions disguise themes from relatively a various spectrum, akin to layout thought, Belyi services, team idea, transitive graphs, commonplace maps, and Hurwitz difficulties, and current the cutting-edge in those components. **Applications of crew conception to Combinatorics** might be important within the examine of graphs, maps and polytopes having maximal symmetry, and is geared toward researchers within the parts of staff idea and combinatorics, graduate scholars in arithmetic, and different experts who use team conception and combinatorics.

**Jack Koolen** teaches on the division of arithmetic at Pohang college of technology and know-how, Korea. His major examine pursuits contain the interplay of geometry, linear algebra and combinatorics, on which he released 60 papers.

**Jin Ho Kwak** is Professor on the division of arithmetic at Pohang college of technology and know-how, Korea, the place he's director of the Combinatorial and Computational arithmetic heart (Com2MaC). He works on combinatorial topology, commonly on masking enumeration relating to Hurwitz difficulties and commonplace maps on surfaces, and released greater than a hundred papers in those areas.

**Ming-Yao Xu** is Professor in division of arithmetic at Peking collage, China. the point of interest in his learn is in finite team idea and algebraic graph concept. Ming-Yao Xu released over eighty papers on those topics.

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**Additional info for Applications of Group Theory to Combinatorics**

**Sample text**

Y. Xu, 1/2-transitive graphs of order 3p, Journal of Algebraic Combinatorics, 3(1994), 347–355. G. -Q. S. Sim, The normality of Cayley graphs of finite Abelian groups with valency 5, Systems Science and Mathematical Sciences, 13(2000), 425–431. G. -Q. S. Y. Xu, On the normality of Cayley graphs of Abelian groups, Algebra Colloquium, 5(1998), 297–304. [5] N. Biggs, Algebraic Graph Theory (second edition), Cambridge University Press, Cambridge, 1993. E. Conder and D. Marušiˇc, A tetravalent half-arc-transitive with non-abelian vertex stabilizer, J.

The previous example was pointed out to us by Michael Orrison who uses the case l = k − 1 in [25] for the analysis of unranked data. He also noticed that it is a special case of clique covers of graphs, that is, covers in which the parts are cliques (complete subgraphs). These arise naturally for edge-transitive graphs as follows. Let be a G-edge transitive graph and let A be a maximal clique. Let G = AG = {Ag |g ∈ G}. Then ( , G ) is a uniform cover which is G-transitive. There are some graphs for which each edge lies in exactly one clique in the G-class of cliques G .

2 Link with linear spaces We now consider decomposing complete graphs into complete subgraphs. A linear space ( , L) is an incidence geometry with point set and line set L where each line is a subset of , |L| ≥ 2, and each pair of points lies on exactly one line. For a linear space ( , L) 35 ∼ Kn be its point graph, that is, the complete graph with vertex set , and let with n = | |, let = P be the set of subgraphs of such that P ∈ P if and only if P is the complete graph whose vertex set consists of all points on some line.

### Applications of Group Theory to Combinatorics by Jack Koolen, Jin Ho Kwak, Ming-Yao Xu

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