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- Hassan Yousefi-Azari, B. Manoochehrian, Ali Reza Ashrafi
- Appl. Math. Lett.
- 2008

The Padmakar–Ivan index of a graph G is the sum over all edges uv of G of number of edges which are not equidistant from u and v. In this work, an exact expression for the PI index of the Cartesian product of bipartite graphs is computed. Using this formula, the PI indices of C4 nanotubes and nanotori are computed. c © 2007 Elsevier Ltd. All rights reserved.

- Hassan Yousefi-Azari, B. Manoochehrian, Ali Reza Ashrafi
- Ars Comb.
- 2007

- B. Manoochehrian, Hassan Yousefi-Azari, Ali Reza Ashrafi
- Ars Comb.
- 2008

In this paper we prove that any distance-balanced graph G with ∆(G) ≥ |V (G)| − 3 is regular. Also we define notion of distancebalanced closure of a graph and we find distance-balanced closures of trees T with ∆(T ) ≥ |V (T )| − 3.

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