On Wiener index and Wiener polarity index of some polyomino chains

Abstract

A graph invariant is a numerical value that depicts the structural properties of an entire graph. The Wiener index is the oldest distance based graph invariant which is defined as the sum of distances between all unordered pair of vertices of the graph G. In this paper we use the method of edge cut to compute the Wiener index and Wiener polarity index of linear (Ln) and zig-zag (Zn) polyomino chains of 4-cycle. Also, we introduce another polyomino chain of 4k-cycle Zmn and calculate its Wiener index and Wiener polarity index for m = 3 and m = 4. Finally, the graphical representation is given to analyze the behavior of these indices.