The PI and vertex PI polynomial of dendimers

Document Type: Original Article

Author

Department of Science, Islamic Azad University, Savadkooh Branch, Savadkooh, Mazandaran, I. R. Iran

Abstract

Let G be a simple connected graph. The vertex PI polynomial of G is defined as PIv(G ,x )=Σe=uv Xnu(e)+nv(e) here nu(e) is the number of vertices closer to u than v and nv(e) is the number of vertices closer to v than u. The PI polynomial of G is defined as  PI(G ,x )=Σe=uv Xmu(e)+mv(e) , 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. In this paper, the PI and vertex PI polynomials of two types of dendrimers are computed.

Graphical Abstract

The PI and vertex PI polynomial of dendimers

Keywords

Main Subjects


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Volume 1, 1-2
Winter and Spring 2011
Pages 59-65
  • Receive Date: 03 January 2011
  • Revise Date: 06 February 2011
  • Accept Date: 15 March 2011