APPLIED SCIENCE & SCIENCE DOMAIN
Published September 1, 2023 | Version v1
Journal article Open

Weighted Vertex PI Index and Polynomial of Some Planar Graphs

Authors/Creators

  • 1. Department of Mathematics, Noorul Islam Centre for Higher Education, Kumaracoil, Tamil Nadu, India

Description

A distance-based molecular structure descriptor is the vertex PI index. The weighted version of the vertex PI index is proposed to broaden the diversity of this topological indicator for graphs. In this article, the weighted vertex PI index and weighted vertex PI polynomial of some planar graphs namely Helm graph, Dumbbell graph, Star graph and Friendship graph are obtained.

Files

Weighted Vertex PI Index and Polynomial.pdf

Files (490.1 kB)

Name Size Download all
md5:a79b62bb1660a9d682458a07fd4494e8
490.1 kB Preview Download

Additional details

References

  • Ilić, A., & Milosavljević, N. (2013). The weighted vertex PI index. Mathematical and Computer Modelling, 57(3-4), 623-631.
  • Ma, G., Bian, Q., & Wang, J. (2019). The weighted vertex PI index of (n, m)-graphs with given diameter. Applied Mathematics and Computation, 354, 329-337.
  • Salahshour, M. A. (2011). The PI and vertex PI Polynomial of dendimers. Journal of Discrete Mathematics and Its Applications, 1(1-2), 59-65.
  • You, L., Zhu, R., & You, Z. (2012). The (weighted) vertex PI index of unicyclic graphs. Match-Communications in Mathematical and Computer Chemistry, 67(2), 383.
  • Yousefi-Azari, H., Manoochehrian, B., & Ashrafi, A. R. (2008). The PI index of product graphs. Applied mathematics letters, 21(6), 624-627.
  • Wang, S., Shao, Z., Liu, J. B., & Wei, B. (2019). The bounds of vertex Padmakar–Ivan index on k-trees. Mathematics, 7(4), 324.
  • Mansour, T., & Schork, M. (2009). The vertex PI index and Szeged index of bridge graphs. Discrete Applied Mathematics, 157(7), 1600-1606.
  • Azari, M., Iranmanesh, A., & Doslic, T. (2016). Vertex-weighted Wiener polynomials of subdivision-related graphs. Opuscula Mathematica, 36(1), 5-23.
  • Ghorbani, M., & Jalali, M. (2009). The vertex PI, szeged and omega polynomials of carbon nanocones CNC4 (n). Match, 62(2), 353.