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Energy Conditions for Hamiltonian and Traceable Graphs

Year 2019, Volume: 2 Issue: 1, 33 - 35, 20.03.2019
https://doi.org/10.32323/ujma.456605

Abstract

A graph is called Hamiltonian (resp. traceable) if the graph has a Hamiltonian cycle (resp. path), a cycle (resp. path) containing all the vertices of the graph. The energy of a graph is defined as the sum of the absolute values of the eigenvalues of the graph. In this note, we present new conditions based on energy for Hamiltonain and traceable graphs.

References

  • [1] J. A. Bondy, U. S. R. Murty, Graph Theory with Applications, The Macmillan Press LTD, 1976.
  • [2] I. Gutman, The energy of a graph, Berichte der Mathematisch-Statistischen Sektion im Forschungszentrum Graz, 103 (1978), 1 – 12.
  • [3] T. Ando, M. Lin, Proof of a conjectured lower bound on the chromatic number of a graph, Linear Algebra Appl., 485 (2015), 480 – 484.
  • [4] D. Cvetkovic, M. Doob, H. Sachs, Spectra of Graphs – Theory and Application, 3rd Edition, Johann Ambrosius Barth, 1995.
  • [5] R. Li, A sharp upper bound for the energy of a connected graph, Manuscript, July 2018.
Year 2019, Volume: 2 Issue: 1, 33 - 35, 20.03.2019
https://doi.org/10.32323/ujma.456605

Abstract

References

  • [1] J. A. Bondy, U. S. R. Murty, Graph Theory with Applications, The Macmillan Press LTD, 1976.
  • [2] I. Gutman, The energy of a graph, Berichte der Mathematisch-Statistischen Sektion im Forschungszentrum Graz, 103 (1978), 1 – 12.
  • [3] T. Ando, M. Lin, Proof of a conjectured lower bound on the chromatic number of a graph, Linear Algebra Appl., 485 (2015), 480 – 484.
  • [4] D. Cvetkovic, M. Doob, H. Sachs, Spectra of Graphs – Theory and Application, 3rd Edition, Johann Ambrosius Barth, 1995.
  • [5] R. Li, A sharp upper bound for the energy of a connected graph, Manuscript, July 2018.
There are 5 citations in total.

Details

Primary Language English
Subjects Mathematical Sciences
Journal Section Articles
Authors

Rao Li

Publication Date March 20, 2019
Submission Date August 31, 2018
Acceptance Date November 29, 2018
Published in Issue Year 2019 Volume: 2 Issue: 1

Cite

APA Li, R. (2019). Energy Conditions for Hamiltonian and Traceable Graphs. Universal Journal of Mathematics and Applications, 2(1), 33-35. https://doi.org/10.32323/ujma.456605
AMA Li R. Energy Conditions for Hamiltonian and Traceable Graphs. Univ. J. Math. Appl. March 2019;2(1):33-35. doi:10.32323/ujma.456605
Chicago Li, Rao. “Energy Conditions for Hamiltonian and Traceable Graphs”. Universal Journal of Mathematics and Applications 2, no. 1 (March 2019): 33-35. https://doi.org/10.32323/ujma.456605.
EndNote Li R (March 1, 2019) Energy Conditions for Hamiltonian and Traceable Graphs. Universal Journal of Mathematics and Applications 2 1 33–35.
IEEE R. Li, “Energy Conditions for Hamiltonian and Traceable Graphs”, Univ. J. Math. Appl., vol. 2, no. 1, pp. 33–35, 2019, doi: 10.32323/ujma.456605.
ISNAD Li, Rao. “Energy Conditions for Hamiltonian and Traceable Graphs”. Universal Journal of Mathematics and Applications 2/1 (March 2019), 33-35. https://doi.org/10.32323/ujma.456605.
JAMA Li R. Energy Conditions for Hamiltonian and Traceable Graphs. Univ. J. Math. Appl. 2019;2:33–35.
MLA Li, Rao. “Energy Conditions for Hamiltonian and Traceable Graphs”. Universal Journal of Mathematics and Applications, vol. 2, no. 1, 2019, pp. 33-35, doi:10.32323/ujma.456605.
Vancouver Li R. Energy Conditions for Hamiltonian and Traceable Graphs. Univ. J. Math. Appl. 2019;2(1):33-5.

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