Extremal tricyclic, tetracyclic, and pentacyclic graphs with respect to the Narumi-Katayama index

Abstract

Let G be an n-vertex graph with the vertex degree sequence d1; d2, …, dn. The Narumi-Katayama index of G is defined as NK(G) = ∏n i=1di. We determine eight classes of n-vertex tricyclic graphs with the fit through the eighth maximal NK index, n ≥ 10. We also identify ten classes of n-vertex tetracyclic graphs with the fit through the ninth maximal NK index, n ≥ 10, and thirteen classes of n-vertex pentacyclic graphs with the fit through the twelfth maximal NK index, n ≥ 12. © 2018, University of Tartu. All right reserved.