Distribution of some graph invariants over hierarchical product of graphs

The hierarchical product of graphs was introduced very recently by L. Barriere et al. in [On the spectra of hypertrees, Linear Algebra Appl. 428 (2008) 1499-1510], and some of its main properties were studied. In this paper, some new properties of this new graph product are investigated. We prove that Gn⊓…⊓G1 is median graph if and only if G1,G2,…,Gn are median. An exact formula for metric dimension of Gn⊓…⊓G1, as well as formulas for the eccentric distance sum and edge revised Szeged of hierarchical product of graphs are presented. Some applications of our results are also presented.