Extremal graphs with respect to the vertex PI index

@article{NadjafiArani2009ExtremalGW,
  title={Extremal graphs with respect to the vertex PI index},
  author={Mohammad J. Nadjafi-Arani and Gholam Hossein Fath-Tabar and Ali Reza Ashrafi},
  journal={Appl. Math. Lett.},
  year={2009},
  volume={22},
  pages={1838-1840}
}
The vertex PI index of a graph G is the sum over all edges uv ∈ E(G) of the number of vertices which are not equidistant to u and v. In this paper, the extremal values of this new topological index are computed. In particular, we prove that for each n-vertex graph G, n(n− 1) ≤ PIv(G) ≤ n · b n 2 c · d n 2 e, where bxc denotes the greatest integer not exceeding x and dxe is the smallest integer not less than x. The extremal graphs with respect to the vertex PI index are also determined. © 2009… CONTINUE READING
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