Abstract
The PI index is a graph invariant defined as the summation of the sums of n e u ( e | G ) and n e v ( e | G ) over all the edges e = u v of a connected graph G , i.e., PI ( G ) = ∑ e ∈ E ( G ) [ n e u ( e | G ) + n e v ( e | G ) ] , where n e u ( e | G ) is the number of edges of G lying closer to u than to v and n e v ( e | G ) is the number of edges of G lying closer to v than to u . An efficient formula for calculating the PI index of polyomino chains is given, and the bounds for the PI index of polyomino chains are established.
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