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Improvement of Sufficient Conditions for Pancyclic Graphs

Xingxing Wang, Mengjie Li, Wenxue Shi, Yue Wu, Yuting Zhao
Scientific Journal of Technology, (2024), Vol.6, No.1, pp.29-32
Published: January 22, 2024
DOI: 10.54691/w10e3408
PDF: Download Full Text PDF
Abstract

The study of cyclic graphs has always been a hot topic in the field of graph theory and has received widespread attention from graph theory practitioners. If an n-order graph G exactly contains cycles of all lengths from 3 to n, then the graph is called a pan cycle graph. This article proves that, after excluding some special cases, when the number of edges in graph G is greater than or equal to C2n-3+12, graph G must be a pan cyclic graph.

Keywords: Pan Circle Diagram; Number of Edges; Spectrum.
APA Citation: Xingxing Wang, Mengjie Li, Wenxue Shi, Yue Wu, Yuting Zhao (2024). Improvement of Sufficient Conditions for Pancyclic Graphs. Scientific Journal of Technology, 6(1), 29-32. https://doi.org/10.54691/w10e3408

References

  1. J.-A. Bondy. Pancyclic graphs I[J]. J. Combin.Theory Ser. B, 1971, 11:80-84.
  2. J.-A. Bondy, U.S.R. Murty, Graph Theory, GTM 244, Springer, New York, 2008.
  3. E. Mitchem, J. Schmeichel, Bipartite graphs with cycles of all even length, J. Graph Theory, 1982, 6 :429-439.
  4. G.-D. Yu, T. Yu, et al. Spectral Sufficient Conditions on Pancyclic Graphs[J]. Complexity, 2021, 1:1-8.
  5. R Li. Spectral Conditions for the Bipancyclic Bipartite Graphs[J]. 2021, 10.48550/ arXiv. 2106.13741.
  6. D. Bauer, E. Schmeichel. Hamiltonian degree conditions which imply a graph is pancyclic[J]. Journal of Combinatorial Theory, 1990, 48(1):111-116.
  7. H Yuan. A bound on the spectral radius of graphs[J]. Linear Algebra Appl, 1988,108:135-139.
  8. L.H. Feng, G.H. Yu, On three conjectures involving the signless Laplacian spectral radius of graphs, Publ. De L Institut Math. 2009, 85: 35-38.
  9. O. Ore, Hamiltonian connected graphs, J Math Pures Appl. 1963, 42 :21-27.
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