On the First Variable Zagreb Index

نویسندگان
Behzadi, M. H. ID 1
Moradian, K. ID 2
Kazemi, R. ID 3

1 Department of Statistics, Islamic Azad University

2 Department of Statistics, Islamic Azad University

3 Imam Khomeini international university

doi
10.22052/ijmc.2017.71544.1262
چکیده

‎The first variable Zagreb index of graph $G$ is defined as‎ ‎\begin{eqnarray*}‎ ‎M_{1,\lambda}(G)=\sum_{v\in V(G)}d(v)^{2\lambda}‎, ‎\end{eqnarray*}‎ ‎where $\lambda$ is a real number and $d(v)$ is the degree of‎ ‎vertex $v$‎. ‎In this paper‎, ‎some upper and lower bounds for the distribution function and expected value of this index in random increasing trees (recursive trees‎, ‎plane-oriented recursive trees and binary increasing trees) are‎ ‎given‎.

کلیدواژه‌ها
First variable Zagreb index‎, ‎Random increasing‎ ‎trees‎, ‎Distribution function‎, ‎Expected value