论文信息 - Unicyclic Graphs with Minimal Energy

Unicyclic Graphs with Minimal Energy

If G is a graph and λ1,λ2,...,λn are its eigenvalues, then the energy of G is defined as E(G)=|λ1|+|λ2|+⋅⋅⋅+|λn|. Let Sn3 be the graph obtained from the star graph with n vertices by adding an edge. In this paper we prove that Sn3 is the unique minimal energy graph among all unicyclic graphs with n vertices (n≥6).

Yaoping Hou | Yaoping Hou

[1] I. Gutman,et al. Mathematical Concepts in Organic Chemistry , 1986 .

[2] I. Outman,et al. Acyclic conjugated molecules, trees and their energies , 1987 .

[3] Ivan Gutman,et al. Acyclic systems with extremal Hückel π-electron energy , 1977 .

[4] I. Gutman. Total π-electron energy of benzenoid hydrocarbons , 1992 .

[5] Pierre Hansen,et al. Variable Neighborhood Search for Extremal Graphs. 2. Finding Graphs with Extremal Energy , 1998, J. Chem. Inf. Comput. Sci..

[6] Pierre Hansen,et al. Variable Neighborhood Search for Extremal Graphs: IV: Chemical Trees with Extremal Connectivity Index , 1998, Comput. Chem..

[7] Pierre Hansen,et al. Variable neighborhood search for extremal graphs: 1 The AutoGraphiX system , 1997, Discret. Math..

[8] Michael Doob,et al. Spectra of graphs , 1980 .

[9] Fuji Zhang,et al. On Acyclic Conjugated Molecules with Minimal Energies , 1999, Discret. Appl. Math..