Computing Reformulated First Zagreb Index of Some Chemical Graphs as an Application of Generalized Hierarchical Product of Graphs

• Main Author: Nilanjan De
• Format: Article
• Language: English
• Published: Ptolemy Scientific Research Press 2018-11-01
• Series: Open Journal of Mathematical Sciences
• Subjects: Topological Index; Zagreb Index; Reformulated Zagreb Index; Graph Operations; Composite graphs; Generalized Hierarchical Product.
• Online Access: https://openmathscience.com/computing-reformulated-first-zagreb-index-of-some-chemical-graphs-as-an-application-of-generalized-hierarchical-product-of-graphs-2/

The generalized hierarchical product of graphs was introduced by L. Barrière et al. in 2009. In this paper, reformulated first Zagreb index of generalized hierarchical product of two connected graphs and hence as a special case cluster product of graphs are obtained. Finally using the derived results the reformulated first Zagreb index of some chemically important graphs such as square comb lattice, hexagonal chain, molecular graph of truncated cube, dimer fullerene, zig-zag polyhex nanotube and dicentric dendrimers are computed.