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## Energy Conditions for Hamiltonian and Traceable Graphs

#### Rao Li [1]

##### 29 69

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.
Energy, Hamiltonian, Graph, Traceable
• [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.
Primary Language en Mathematics Articles Author: Rao Li (Primary Author)Country: United States
 Bibtex @research article { ujma456605, journal = {Universal Journal of Mathematics and Applications}, issn = {2619-9653}, address = {Emrah Evren KARA}, year = {2019}, volume = {2}, pages = {33 - 35}, doi = {10.32323/ujma.456605}, title = {Energy Conditions for Hamiltonian and Traceable Graphs}, key = {cite}, author = {Li, Rao} } APA Li, R . (2019). Energy Conditions for Hamiltonian and Traceable Graphs. Universal Journal of Mathematics and Applications, 2 (1), 33-35. DOI: 10.32323/ujma.456605 MLA Li, R . "Energy Conditions for Hamiltonian and Traceable Graphs". Universal Journal of Mathematics and Applications 2 (2019): 33-35 Chicago Li, R . "Energy Conditions for Hamiltonian and Traceable Graphs". Universal Journal of Mathematics and Applications 2 (2019): 33-35 RIS TY - JOUR T1 - Energy Conditions for Hamiltonian and Traceable Graphs AU - Rao Li Y1 - 2019 PY - 2019 N1 - doi: 10.32323/ujma.456605 DO - 10.32323/ujma.456605 T2 - Universal Journal of Mathematics and Applications JF - Journal JO - JOR SP - 33 EP - 35 VL - 2 IS - 1 SN - 2619-9653- M3 - doi: 10.32323/ujma.456605 UR - https://doi.org/10.32323/ujma.456605 Y2 - 2018 ER - EndNote %0 Universal Journal of Mathematics and Applications Energy Conditions for Hamiltonian and Traceable Graphs %A Rao Li %T Energy Conditions for Hamiltonian and Traceable Graphs %D 2019 %J Universal Journal of Mathematics and Applications %P 2619-9653- %V 2 %N 1 %R doi: 10.32323/ujma.456605 %U 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