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Erschienen in:
22.01.2021
The balanced double star has maximum exponential second Zagreb index
Erschienen in: Journal of Combinatorial Optimization | Ausgabe 2/2021
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Abstract
The exponential of the second Zagreb index of a graph G with n vertices is defined as where \(m_{i,j}\) is the number of edges joining vertices of degree i and j. It is well known that among all trees with n vertices, the path has minimum value of \(e^{M_{2}}\). In this paper we show that the balanced double star tree has maximum value of \(e^{{\mathcal {M}}_{2}}\).
$$\begin{aligned} e^{{\mathcal {M}}_{2}}\left( G\right) =\sum _{1\le i\le j\le n-1}m_{i,j}\left( G\right) e^{ij}, \end{aligned}$$