Energy Conditions for Hamiltonian and Traceable Graphs

Year 2019, Volume: 2 Issue: 1, 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.