Abstract
If G is a graph and λ1,λ2,...,λ n are its eigenvalues, then the energy of G is defined as E(G)=|λ1|+|λ2|+⋅⋅⋅+|λ n |. Let S n 3 be the graph obtained from the star graph with n vertices by adding an edge. In this paper we prove that S n 3 is the unique minimal energy graph among all unicyclic graphs with n vertices (n≥6).
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References
I. Gutman and O.E. Polansky, Mathematical Concepts in Organic Chemistry (Springer, Berlin, 1986).
I. Gutman, Total π-electron energy of benzenoid hydrocarbon, Topic Curr. Chem. 162(1992) 29–63.
I. Gutman, Acyclic systems with extremal Huckel π-electron energy, Theor. Chim. Acta 45(1977) 79–87.
I. Gutman, Acyclic conjugated molecules, trees and their energies, J. Math. Chem. 2(1987) 123–143.
G. Caporossi and P. Hansen, Variable neighborhood search for extremal graphs. 1. The AutoGraphix system, Discrete Math. 212(2000) 29–49.
L. Turker, An upper bound for total π-electron energy of alternant hydrocarbons, Commun. Math. Chem. 6(1984) 83–94.
F. Zhang and H. Li, On acyclic conjugated molecules with minimal energies, Discrete Appl. Math. 92 (1999) 71–84.
G. Caporossi, D. Cvetkovic, I. Gutman and P. Hansen, Variable neighborhood search for extremal graphs. 2. Finding graphs with extremal energy, J. Chem. Inform. Comput. Sci. 39(1999) 984–996.
D. Cvetkovic, M. Doob and H. Sachs, Spectra of Graphs (Academic Press, New York, 1980).
I. Gutman and Y. Hou, Bipartite unicyclic graphs with greatest energy, MATCH 43(2001) 17–28.
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Hou, Y. Unicyclic Graphs with Minimal Energy. Journal of Mathematical Chemistry 29, 163–168 (2001). https://doi.org/10.1023/A:1010935321906
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DOI: https://doi.org/10.1023/A:1010935321906