First and second extremal bipartite graphs with respect to PI index
2011
Yarahmadi, Z. | Ashrafi, A.R. | Gutman, I.
The Padmakar–Ivan (PI) index of a graph G is defined as the sum of terms [mᵤ(e)+mᵥ(e)] over all edges of G, where e is an edge, connecting the vertices u and v, where mᵤ(e) is the number of edges of G lying closer to the vertex u than to the vertex v, and where mᵥ(e) is defined analogously. The extremal values of the PI index are determined in the class of connected bipartite graphs with a given number of edges.
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