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16. 12. 2013.
On the Narumi-Katayama Index of Composite Graphs
The Narumi-Katayama index of a graph $G$, denoted by $NK(G)$, is equal to the product of degrees of vertices of G. In this paper we investigate its behavior under several binary operations on graphs. We present explicit formulas for its values for composite graphs in terms of its values for operands and some auxiliary invariants. We demonstrate applications of our results to several chemically relevant classes of graphs and show how the Narumi-Katayama index can be used as a measure of graph irregularity.