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AIMS Mathematics

2020, Volume 5, Issue 6: 5389-5401. doi: 10.3934/math.2020346
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Research article

Some spectral sufficient conditions for a graph being pancyclic

  • 1.
    Department of Public Education, Hefei Preschool Education College, Hefei 230013, China
  • 2.
    School of Mathmatics and Physics, Anqing Normal University, Anqing 246133, China
  • 3.
    Department of Information Technology, Faculty of Computing and Information Technology, King Abdulaziz University, Jeddah 21589, Saudi Arabia
  • 4.
    School of Mathematics, Southeast University, Nanjing 210096, China
  • Received: 10 February 2020 Accepted: 16 June 2020 Published: 23 June 2020

  • MSC : 05C50, 15A18

  • Let $G(V, E)$ be a simple connected graph of order $n$. A graph of order $n$ is called pancyclic if it contains all the cycles $C_k$ for $k\in \{3, 4, \cdot\cdot\cdot, n\}$. In this paper, some new spectral sufficient conditions for the graph to be pancyclic are established in terms of the edge number, the spectral radius and the signless Laplacian spectral radius of the graph.

    Citation: Huan Xu, Tao Yu, Fawaz E. Alsaadi, Madini Obad Alassafi, Guidong Yu, Jinde Cao. Some spectral sufficient conditions for a graph being pancyclic[J]. AIMS Mathematics, 2020, 5(6): 5389-5401. doi: 10.3934/math.2020346

    Related Papers:

  • Let $G(V, E)$ be a simple connected graph of order $n$. A graph of order $n$ is called pancyclic if it contains all the cycles $C_k$ for $k\in \{3, 4, \cdot\cdot\cdot, n\}$. In this paper, some new spectral sufficient conditions for the graph to be pancyclic are established in terms of the edge number, the spectral radius and the signless Laplacian spectral radius of the graph.


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    [1] M. Fiedler, V. Nikiforov, Spectral radius and Hamiltonicity of graphs, Linear Algebra Appl., 432 (2010), 2170-2173. doi: 10.1016/j.laa.2009.01.005
    [2] G. D. Yu, Y. Z. Fan, Spectral conditions for a graph to be hamilton-connected, Appl. Mech. Mater., 336-338 (2013), 2329-2334.
    [3] M. Lu, H. Q. Liu, F. Tian, Spectral Radius and Hamiltonion graphs, Linear Algebra Appl., 437 (2012), 1670-1674. doi: 10.1016/j.laa.2012.05.021
    [4] Y. Z. Fan, G. D. Yu. Spectral Condition for a Graph to be Hamiltonian with respect to Normalized Laplacian, Mathematics, 2012.
    [5] L. H. Feng, P. L. Zhang, H. Liu, et al. Spectral conditions for some graphical properties, Linear Algebra Appl., 524 (2017), 182-198. doi: 10.1016/j.laa.2017.03.006
    [6] B. L. Li, B. Ning, Spectral analogues of Erdos' and Moon-Moser's theorems on Hamilton cycles, Linear Multilinear Algebra, 64 (2016), 2252-2269. doi: 10.1080/03081087.2016.1151854
    [7] R. F. Liu, W. C. Shiu, J. Xue, Sufficient spectral conditions on Hamiltonian and traceable graphs, Linear Algebra Appl., 467 (2015), 254-266. doi: 10.1016/j.laa.2014.11.017
    [8] V. Nikiforov, Spectral radius and Hamiltonicity of graphs with large minimum degree, Czechoslovak Math. J., 66 (2016), 925-940. doi: 10.1007/s10587-016-0301-y
    [9] G. D. Yu, G. X. Cai, M. L. Ye, et al. Energy conditions for Hamiltonicity of graphs, Discrete Dyn. Nature Soc., 53-56 (2014), 1-6.
    [10] Q. N. Zhou, L. G. Wang, Y. Lu, Some sufficient conditions on hamiltonian and traceable graphs, Advances in Mathematics, 47 (2018), 31-40.
    [11] G. D. Yu, T. Yu, A. X. Shu, et al. Some Sufficient Conditions on Pancyclic Graphs, Inf. Process. Lett., 2018.
    [12] E. F. Schmeichel, S. L. Hakimi, Pancyclic graphs and a conjecture of Bondy and Chvatal, J. Comb. Theory, 17 (1974), 22-34. doi: 10.1016/0095-8956(74)90043-4
    [13] H. Yuan. A bound on the spectral radius of graphs, Linear Algebra and Its Applications, 108 (1988), 135-139.
    [14] G. D. Yu, Y. Z. Fan, Spectral Conditions for a Graph to be Hamilton-Connected, Applied Mech. Mater., 336-338 (2013), 2329-2334.
    [15] J. A. Bondy, A. W. Ingleton, Pancyclic graphs I, J. Comb. Theory, 11 (1971), 80-84. doi: 10.1016/0095-8956(71)90016-5
    [16] R. Haggkvist, R. J. Faudree, R. H. Schelp, Pancyclic graphs Dconnected Ramsey number, Ars Comb.-Waterloo Winnipeg, 11 (1981), 37-49.
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  • © 2020 the Author(s), licensee AIMS Press. This is an open access article distributed under the terms of the Creative Commons Attribution License (http://creativecommons.org/licenses/by/4.0)
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