论文信息 - Some properties of the first general Zagreb index

Some properties of the first general Zagreb index

In this paper, the effects on the first general Zagreb index are observed when some operations, such as edge moving, edge separating and edge switching are applied to the graphs. Moreover, we obtain the majorization theorem to the first general Zagreb indices between two graphic sequences. Furthermore, we illustrate the application of these new properties, and obtain the largest or smallest first general Zagreb indices among some class of connected graphs.

Bolian Liu | Muhuo Liu

[1] Ch. Das. SHARP BOUNDS FOR THE SUM OF THE SQUARES OF THE DEGREES OF A GRAPH , 2003 .

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

[3] M. Randic. Novel molecular descriptor for structure—property studies , 1993 .

[4] R. Jackson. Inequalities , 2007, Algebra for Parents.

[5] Kinkar Chandra Das,et al. Maximizing the sum of the squares of the degrees of a graph , 2004, Discret. Math..

[6] I. Gutman,et al. Graph theory and molecular orbitals. Total φ-electron energy of alternant hydrocarbons , 1972 .

[7] Shenggui Zhang,et al. Bicyclic graphs with the first three smallest and largest values of the first general Zagreb index , 2006 .

[8] Dominique de Caen,et al. An upper bound on the sum of squares of degrees in a graph , 1998, Discret. Math..

[9] N. Trinajstic. Xueliang Li, Ivan Gutman: Mathematical Aspects of Randić-type Molecular Structure Descriptors , 2006 .

[10] Yongtang Shi,et al. ON MOLECULAR GRAPHS WITH SMALLEST AND GREATEST ZEROTH-ORDER GENERAL RANDIĆ INDEX∗ , 2022 .

[11] Bo Zhou,et al. Relations between Wiener, hyper-Wiener and Zagreb indices , 2004 .