The PI and vertex PI polynomial of dendimers

Document Type : Full Length 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

References

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Journal of Discrete Mathematics and Its Applications
Volume 1, 1-2
June 2011
Pages 59-65

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History

  • Receive Date: 03 January 2011
  • Revise Date: 06 February 2011
  • Accept Date: 15 March 2011
  • Publish Date: 01 June 2011

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