# On Some Cycles in Wenger Graphs

@article{Wang2020OnSC, title={On Some Cycles in Wenger Graphs}, author={Ye Wang and Felix Lazebnik and Andrew Thomason}, journal={Acta Mathematicae Applicatae Sinica, English Series}, year={2020}, volume={36}, pages={492-502} }

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

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#### References

SHOWING 1-10 OF 40 REFERENCES

On the Diameter of Wenger Graphs

- Mathematics
- 2008

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 two… Expand

On the spectrum of Wenger graphs

- Computer Science, Mathematics
- J. Comb. Theory, Ser. B
- 2014

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

- Mathematics
- 2008

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 length… Expand

New Examples of Graphs without Small Cycles and of Large Size

- Computer Science, Mathematics
- Eur. J. Comb.
- 1993

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

- Mathematics
- 2013

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 in… Expand

A note on the Turán function of even cycles

- Mathematics
- 2010

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 open… Expand

An infinite series of regular edge- but not vertex-transitive graphs

- Mathematics
- 2002

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 defined… Expand

Cycle lengths in sparse graphs

- Mathematics, Computer Science
- Comb.
- 2008

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

- Mathematics
- 1974

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 l… Expand

An infinite series of regular edge- but not vertex-transitive graphs

- Computer Science
- J. Graph Theory
- 2002

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