Energy Conditions for Hamiltonian and Traceable Graphs

Rao Li

doi:10.32323/ujma.456605

Research Article

Energy Conditions for Hamiltonian and Traceable Graphs

Year 2019, , 33 - 35, 20.03.2019

Rao Li

https://doi.org/10.32323/ujma.456605

Cited By: 2

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.

Keywords

Energy, Hamiltonian, Graph, Traceable

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, , 33 - 35, 20.03.2019

Rao Li

https://doi.org/10.32323/ujma.456605

Cited By: 2

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

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.