IEEE Access | |
Computing Zagreb Indices of the Subdivision-Related Generalized Operations of Graphs | |
Hafiz Muhammad Awais1  Muhammad Javaid1  Jia-Bao Liu2  | |
[1] Department of Mathematics, School of Science, University of Management and Technology, Lahore, Pakistan;School of Mathematics and Physics, Anhui Jianzhu University, Hefei, China; | |
关键词:
Molecular structures;
subdivision operations;
generalized |
|
DOI : 10.1109/ACCESS.2019.2932002 | |
来源: DOAJ |
【 摘 要 】
Mathematical modeling or numerical coding of the molecular structures play a significant role in the studies of the quantitative structure-activity relationships (QSAR) and quantitative structures property relationships (QSPR). In 1972, the entire energy of π-electron of a molecular graph is computed by the addition of square of degrees (valencies) of its vertices (nodes). Later on, this computational result was called by the first Zagreb index and became well studied topological index in the field of molecular graph theory. In this paper, for k ∈ N (set of counting numbers), we define four subdivision-related operations of graphs in their generalized form named by Sk, Rk, Qk and Tk. Moreover, using these operations and the concept of the cartesian product of graphs, we construct the generalized Fk-sum graphs Γ1+Fk Γ2, where Fk ∈ {Sk, Rk, Qk, Tk} and Γi are any connected graphs for i ∈ {1, 2}. Finally, the first and second Zagreb indices are computed for the generalized Fk-sum graphs in terms of their factor graphs. In fact, the obtained results are a general extension of the results Eliasi et al. and Deng et al. who studied these operations for exactly k = 1 and computed the Zagreb indices for only F1-sum graphs respectively.
【 授权许可】
Unknown