Improvement of Sufficient Conditions for Pancyclic Graphs
DOI:
https://doi.org/10.54691/w10e3408Keywords:
Pan Circle Diagram; Number of Edges; Spectrum.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.
Downloads
References
J.-A. Bondy. Pancyclic graphs I[J]. J. Combin.Theory Ser. B, 1971, 11:80-84.
J.-A. Bondy, U.S.R. Murty, Graph Theory, GTM 244, Springer, New York, 2008.
E. Mitchem, J. Schmeichel, Bipartite graphs with cycles of all even length, J. Graph Theory, 1982, 6 :429-439.
G.-D. Yu, T. Yu, et al. Spectral Sufficient Conditions on Pancyclic Graphs[J]. Complexity, 2021, 1:1-8.
R Li. Spectral Conditions for the Bipancyclic Bipartite Graphs[J]. 2021, 10.48550/ arXiv. 2106.13741.
D. Bauer, E. Schmeichel. Hamiltonian degree conditions which imply a graph is pancyclic[J]. Journal of Combinatorial Theory, 1990, 48(1):111-116.
H Yuan. A bound on the spectral radius of graphs[J]. Linear Algebra Appl, 1988,108:135-139.
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.
O. Ore, Hamiltonian connected graphs, J Math Pures Appl. 1963, 42 :21-27.
Downloads
Published
Issue
Section
License
This work is licensed under a Creative Commons Attribution-NonCommercial 4.0 International License.
How to Cite
