论文信息 - Extremal Matching Energy of Bicyclic Graphs

Extremal Matching Energy of Bicyclic Graphs

The energy of a graph G is equal to the sum of the absolute values of the eigenvalues of G. Recently, Gutman and Wagner proposed the concept of the matching energy (ME) and pointed out that the chemical applications of ME go back to the 1970s. Let G be a simple graph of order n and 1; 2;:::; n be the roots of its matching polynomial. The matching energy is dened as the sum ∑ n=0 | i|. In this paper, we characterize the graphs with the extremal matching energy among all bicyclic graphs, and completely determine the graphs with the minimal and maximal matching energy in bicyclic graphs.

[1] I. Gutman,et al. Graph theory and molecular orbitals. 19. Nonparametric resonance energies of arbitrary conjugated systems , 1977 .

[2] Yongtang Shi,et al. Solution to a conjecture on the maximal energy of bipartite bicyclic graphs , 2010, 1101.0058.

[3] Frank Harary,et al. Graph Theory , 2016 .

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

[5] Yongtang Shi,et al. Complete solution to a problem on the maximal energy of unicyclic bipartite graphs , 2010, 1010.6129.

[6] E. J. Farrell,et al. An introduction to matching polynomials , 1979, J. Comb. Theory, Ser. B.

[7] Stephan G. Wagner,et al. The matching energy of a graph , 2012, Discret. Appl. Math..

[8] I. Gutman. The Energy of a Graph: Old and New Results , 2001 .

[9] Yongtang Shi,et al. Complete Solution to a Conjecture on the Fourth Maximal Energy Tree , 2011 .

[10] Shengjin Ji,et al. An Approach to the Problem of the Maximal Energy of Bicyclic Graphs , 2011 .

[11] Anton Betten,et al. Algebraic Combinatorics and Applications : Proceedings , 2001 .

[12] Xueliang Li,et al. Complete solution to a conjecture on the maximal energy of unicyclic graphs , 2010, Eur. J. Comb..

[13] D. Cvetkovic,et al. Graph theory and molecular orbitals , 1974 .

[14] J. Aihara. A new definition of Dewar-type resonance energies , 1976 .