On Some Cycles in Wenger Graphs

  title={On Some Cycles in Wenger Graphs},
  author={Ye Wang and F. Lazebnik and A. Thomason},
  journal={Acta Mathematicae Applicatae Sinica, English Series},
Let p be a prime, q be a power of p , and let F q be the field of q elements. For any positive integer n , the Wenger graph W n(q) is defined as follows: it is a bipartite graph with the vertex partitions being two copies of the ( n + 1)-dimensional vector space $$\mathbb{F}_q^{n+1}$$ F q n + 1 , and two vertices p = ( p (1),..., p ( n +1)) and l = [ l (1),..., l ( n +1)] being adjacent if p +1( i ) = p (1) l (1) i −1 , for all i = 2, 3, …, n + 1. In 2008, Shao, He and Shan showed that for n… Expand
2 Citations

Tables from this paper

Extended Wenger Graphs
Author(s): Porter, Michael B. | Advisor(s): Wan, Daqing | Abstract: Wenger graphs were originally introduced as examples of dense graphs that do not have cycles of a given size. Graphs with similarExpand
Graphs without theta subgraphs
A lower bound of order n 5 / 4 is given on the greatest number of edges of any n-vertex θ 3 , 4 -free graph, matching an earlier upper bound by Faudree and Simonovits up to an absolute constant factor. Expand


On the Diameter of Wenger Graphs
AbstractLet q be a prime power, $\mathbb{F}_{q}$ the field of q elements, and n≥1 a positive integer. The Wenger graph Wn(q) is defined as follows: the vertex set of Wn(q) is the union of twoExpand
On the spectrum of Wenger graphs
All distinct eigenvalues of the adjacency matrix of W m ( q ) and their multiplicities are determined and the results on Wenger graphs are surveyed. Expand
The existence of even cycles with specific lengths in Wenger’s graph
Wenger’s graph Hm(q) is a q-regular bipartite graph of order 2qm constructed by using the m-dimensional vector space Fqm over the finite field Fq. The existence of the cycles of certain even lengthExpand
New Examples of Graphs without Small Cycles and of Large Size
A new infinite series of bipartite q-regular edge-transitive graphs of order 2q5 and girth 10 is constructed, 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. Expand
A construction for infinite families of semisymmetric graphs revealing their full automorphism group
We give a general construction leading to different non-isomorphic families $\varGamma_{n,q}(\mathcal{K})$ of connected q-regular semisymmetric graphs of order 2qn+1 embedded inExpand
A note on the Turán function of even cycles
The Tur´an function ex(n, F) is the maximum number of edges in an F-free graph on n vertices. The question of estimating this function for F = C2k, the cycle of length 2k, is one of the central openExpand
An infinite series of regular edge- but not vertex-transitive graphs
Let n be an integer and q be a prime power. Then for any 3 ≤ n ≤ q-1, or n=2 and q odd, we construct a connected q-regular edge-but not vertex-transitive graph of order 2qn+1. This graph is definedExpand
Cycle lengths in sparse graphs
The result improves all previously known lower bounds on the length of the longest cycle and shows that Ω ` d (g−1)/2 is a lower bound for the number of odd cycle lengths in a graph of chromatic number d and girth g. Expand
Cycles of even length in graphs
Abstract In this paper we solve a conjecture of P. Erdos by showing that if a graph G n has n vertices and at least 100kn 1+ 1 k edges, then G contains a cycle C 2 l of length 2 l for every integer lExpand
An infinite series of regular edge- but not vertex-transitive graphs
A connected q-regular edgebut not vertextransitive graph of order 2qn+1 is constructed via a system of equations over the finite field of q elements. Expand