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Extremal graphs with respect to the vertex PI index

✍ Scribed by M.J. Nadjafi-Arani; G.H. Fath-Tabar; A.R. Ashrafi

Publisher
Elsevier Science
Year
2009
Tongue
English
Weight
377 KB
Volume
22
Category
Article
ISSN
0893-9659

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✦ Synopsis

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

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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