<abstract xmlns="http://www.w3.org/1999/xhtml">A topological index of a graph G is a numeric quantity related to <italic>G</italic> which is invariant under automorphisms of G. The Padmakar-Ivan (PI) index of a graph <italic>G</italic> is defined as <italic>PI</italic>(<italic>G</italic>) = Σ<italic>e</italic>=<italic>uv</italic>∈<italic>E</italic>(<italic>G</italic>) [<italic>nu</italic> + <italic>nv</italic>], where <italic>nu</italic> is the number of edges of <italic>G</italic> lying closer to <italic>v</italic> than <italic>u</italic>, analogously <italic>nv</italic>. In this paper, we compute the vertex PI index of <italic>Titania carbon Nanotubes TiO</italic>2[<italic>m</italic>,<italic>n</italic>].</abstract>

A topological index of a graph G is a numeric quantity related to G which is invariant under automorphisms of G. The Padmakar-Ivan (PI) index of a graph G is defined as PI(G) = Σe=uv∈E(G) [nu + nv], where nu is the number of edges of G lying closer to v than u, analogously nv. In this paper, we compute the vertex PI index of Titania carbon Nanotubes TiO2[m,n].

Vertex PI<italic>v</italic> Topological Index of Titania Carbon Nanotubes <italic>TiO</italic>2<italic>(m,n)</italic>

National University of Sciences and Technology

Applied Mathematics and Nonlinear Sciences

This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 3.0 License.

Vertex PI Topological Index of Titania Carbon Nanotubes 

A topological index of a graph G is a numeric quantity related to G which is invariant under automorphisms of G. The Padmakar-Ivan (PI) index of a graph G is...

Vertex PI_v Topological Index of Titania Carbon Nanotubes TiO₂(m,n)

Published Online: Feb 04, 2016

Page range: 175 - 182

Received: Oct 18, 2015

Accepted: Jan 31, 2016

DOI: https://doi.org/10.21042/AMNS.2016.1.00013

© 2016 Mohammad Reza Farahani, Muhammad Kamran Jamil, Muhammad Imran, published by Sciendo

This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 3.0 License.

Fig. 1

Fig. 2

Vertex PIv Topological Index of Titania Carbon Nanotubes TiO2(m,n)

Published Online: Feb 04, 2016

Page range: 175 - 182

Received: Oct 18, 2015

Accepted: Jan 31, 2016

DOI: https://doi.org/10.21042/AMNS.2016.1.00013

© 2016 Mohammad Reza Farahani, Muhammad Kamran Jamil, Muhammad Imran, published by Sciendo

This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 3.0 License.

Fig. 1

Fig. 2

Vertex PI_v Topological Index of Titania Carbon Nanotubes TiO₂(m,n)