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- W2189571961 abstract "Let G be a simple connected graph. We denote the vertex set and the edge set of a graph G by V(G) and E(G), respectively. For notation and graph theory terminology not presented here, we follow [1-7]. Let G be a graph and P is a property on G. A counting polynomial for G is a polynomial as P(G, x) = ∑kP(G, k)x, where P(G, k) is the frequency of occurrence of the property P of length k and x is simply a parameter to hold k [3]. A topological index of a graph is a number related to a graph which is invariant under graph automorphisms. It is easy to see that every topological index defines a counting polynomial and vice versa. The simplest topological indices are the number of vertices and edges of the graph. The Wiener index (W) is the oldest topological indices [12,13]. Let G be a simple graph. The PI(G) defined as = ) (G PI ∑ = + uv e v u m m . Where mu(e) is the number of edges closer to u than v and mv(e) is the number of edges closer to v than u[8]. The PI polynomial of G defined as ∑ = = uv e mu x x G PI ) , ( + e m e v ) ( ) ( . It is clear that the derivation of" @default.
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- W2189571961 date "2009-01-01" @default.
- W2189571961 modified "2023-09-27" @default.
- W2189571961 title "THE PI AND VERTEX PI POLYNOMIAL OF A T-BENZYL-TERMINATED AMIDE-BASED DENDRIMERS" @default.
- W2189571961 hasPublicationYear "2009" @default.
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