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Paper   IPM / M / 11340
School of Mathematics
  Title:   Extremal graphs with respect to the vertex PI index
  Author(s):  A. R. Ashrafi (Joint with M. J. Nadjafi and g. H. Fath-Tabar)
  Status:   Published
  Journal: Appl. Math. Lett.
  Vol.:  22
  Year:  2009
  Pages:   1838-1840
  Supported by:  IPM
The vertex PI index of a graph G is the sum over all edges uvE(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.[[(n)/2]].[[(n)/2]] , where ⎣x⎦ denotes the greatest integer not exceeding x and ⎡x⎤ is the smallest integer not less than x. The extremal graphs with respect to the vertex PI index are also determined.

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