Paper Info
Title
New examples of graphs without small cycles and of large size
Abstract
For any prime power q 3, we consider two infinite series of bi- partite q-regular edge-transitive graphs of orders 2q 3 and 2q 5 which are induced subgraphs of regular generalized 4-gon and 6-gon, respectively. We compare these two series with two families of graphs, H3(p) and H5(p), p is a prime, constructed recently by Wenger ((26)), which are new examples of extremal graphs without 6- and 10-cycles respectively. We prove that the first series contains the family H3(p) for q = p 3. Then we show that no member of the second family H5(p) is a subgraph of a generalized 6-gon. Then, for infinitely many values of q, we construct a new infinite series of bipartite q-regular edge-transitive graphs of order 2q5 and girth 10. Finally, for any prime power q 3, we construct a new infinite series of bipartite q-regular edge-transitive graphs of order 2q9 and girth g 14. Our constructions were motivated by some results on embeddings of Chevalley group geometries in the corresponding Lie algebras and a construction of a blow-up for an incident system and a graph.
Year
DOI
Venue
1993
10.1006/eujc.1993.1048
Eur. J. Comb.
Keywords
Field
DocType
small cycle,large size,new example,infinite series,lie algebra
Prime (order theory),Discrete mathematics,Odd graph,Indifference graph,Combinatorics,Bipartite graph,Chordal graph,Cycle graph,Regular graph,Prime power,Mathematics
Journal
Volume
Issue
ISSN
14
5
0195-6698
Citations 
PageRank 
References 
28
6.04
2
Authors
2
Name
Order
Citations
PageRank
Felix Lazebnik135349.26
Vasiliy A. Ustimenko213619.39