ON SOME TOPOLOGICAL INDICES OF THE GENERALIZED HIERARCHICAL PRODUCT OF GRAPHS

Freydoon  RAHBARNIA; Mostafa  TAVAKOLI; Ali Reza  ASHRAFI

Authors

Freydoon RAHBARNIA Department of Mathematics, Ferdowsi University of Mashhad, Mashhad, Iran. Email: rahbarnia@ferdowsi.um.ac.ir. https://orcid.org/0000-0002-0042-7448
Mostafa TAVAKOLI Department of Mathematics, Ferdowsi University of Mashhad, Mashhad, Iran. Corresponding author: rahbarnia@ferdowsi.um.ac.ir. https://orcid.org/0000-0002-3315-1759
Ali Reza ASHRAFI Department of Mathematics, Faculty of Mathematical Sciences; Department of Nanocomputing, Institute of Nanoscience and Nanotechnology, University of Kashan, Iran. Corresponding author: rahbarnia@ferdowsi.um.ac.ir.

Keywords:

Generalized hierarchical product, Cartesian product, Revised Szeged index, Zagreb indices

Abstract

The generalized hierarchical product of graphs was introduced very recently by L. Barriére et al. In this paper, revised Szeged and new version of Zagreb indices of generalized hierarchical product of two connected graphs are obtained. Using the results obtained here, some known results are deduced as corollaries. Finally, we obtain the Sz^*, M^*₁ and M^*₂ indices of the zig-zag polyhex nanotube TUHC₆[2n, 2], linear phenylene F_n, hexagonal chain L_n and truncated cube as a consequence of our results.

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