Sharp lower bounds on the Narumi–Katayama index of graph operations

The Narumi–Katayama index NK(G)NK(G) of a simple graph G is equal to the product of the degrees of the vertices of G. In this paper, we present sharp lower bounds on the Narumi–Katayama index of several graph operations such as union, join, suspension, rooted product, cluster, corona product, direct product, Cartesian product, strong product, generalized hierarchical product, composition, disjunctive product and symmetric difference in terms of the Narumi–Katayama indices and the orders of their components. Using these results, the Narumi–Katayama index of several classes of graphs will be computed.