The Redefined First, Second and Third Zagreb Indices of Titania Nanotubes TiO2[m,n]

نویسندگان

  • Wei Gao
  • Mohammad R. Farahani
  • Muhammad K. Jamil
  • Muhammad K. Siddiqui
چکیده

School of Information Science and Technology, Yunnan Normal University, Kunming 650500, China Department of Applied Mathematics, Iran University of Science and Technology (IUST) Narmak, Tehran, 16844, Iran Department of Mathematics, Riphah Institute of Computing and Applied Sciences (RICAS) Riphah International University, 14 Ali Road Lahore, Pakistan Department of Mathematics, Comsats Institute of Information Technology, Sahiwal, Pakistan

برای دانلود متن کامل این مقاله و بیش از 32 میلیون مقاله دیگر ابتدا ثبت نام کنید

ثبت نام

اگر عضو سایت هستید لطفا وارد حساب کاربری خود شوید

منابع مشابه

Zagreb, multiplicative Zagreb Indices and Coindices of ‎graphs

‎Let G=(V,E) be a simple connected graph with vertex set V and edge set E. The first, second and third Zagreb indices of G are respectivly defined by: $M_1(G)=sum_{uin V} d(u)^2, hspace {.1 cm} M_2(G)=sum_{uvin E} d(u).d(v)$ and $ M_3(G)=sum_{uvin E}| d(u)-d(v)| $ , where d(u) is the degree of vertex u in G and uv is an edge of G connecting the vertices u and v. Recently, the first and second m...

متن کامل

Note on multiple Zagreb indices

The Zagreb indices are the oldest graph invariants used in mathematical chemistry to predict the chemical phenomena. In this paper we define the multiple versions of Zagreb indices based on degrees of vertices in a given graph and then we compute the first and second extremal graphs for them.

متن کامل

Leap Zagreb indices of trees and unicyclic graphs

By d(v|G) and d_2(v|G) are denoted the number of first and second neighborsof the vertex v of the graph G. The first, second, and third leap Zagreb indicesof G are defined asLM_1(G) = sum_{v in V(G)} d_2(v|G)^2, LM_2(G) = sum_{uv in E(G)} d_2(u|G) d_2(v|G),and LM_3(G) = sum_{v in V(G)} d(v|G) d_2(v|G), respectively. In this paper, we generalizethe results of Naji et al. [Commun. Combin. Optim. ...

متن کامل

TiO2 Nanotubes: Recent Advances in Synthesis and Gas Sensing Properties

Synthesis--particularly by electrochemical anodization-, growth mechanism and chemical sensing properties of pure, doped and mixed titania tubular arrays are reviewed. The first part deals on how anodization parameters affect the size, shape and morphology of titania nanotubes. In the second part fabrication of sensing devices based on titania nanotubes is presented, together with their most no...

متن کامل

On multiplicative Zagreb indices of graphs

Todeschini et al. have recently suggested to consider multiplicative variants of additive graph invariants, which applied to the Zagreb indices would lead to the multiplicative Zagreb indices of a graph G, denoted by ( ) 1  G and ( ) 2  G , under the name first and second multiplicative Zagreb index, respectively. These are define as     ( ) 2 1 ( ) ( ) v V G G G d v and ( ) ( ) ( ) ( ) 2...

متن کامل

ذخیره در منابع من


  با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید

برای دانلود متن کامل این مقاله و بیش از 32 میلیون مقاله دیگر ابتدا ثبت نام کنید

ثبت نام

اگر عضو سایت هستید لطفا وارد حساب کاربری خود شوید

عنوان ژورنال:

دوره   شماره 

صفحات  -

تاریخ انتشار 2016