# On the first variable Zagreb index

Document Type: Research Paper

Authors

1 Department of Statistics, Islamic Azad University

2 Imam Khomeini international university

Abstract

‎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.

Keywords

Main Subjects

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