The balanced double star has maximum exponential second Zagreb index

Roberto Cruz (), Juan Daniel Monsalve () and Juan Rada ()
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Roberto Cruz: Universidad de Antioquia
Juan Daniel Monsalve: Universidad de Antioquia
Juan Rada: Universidad de Antioquia

Journal of Combinatorial Optimization, 2021, vol. 41, issue 2, No 15, 544-552

Abstract: Abstract The exponential of the second Zagreb index of a graph G with n vertices is defined as $$\begin{aligned} e^{{\mathcal {M}}_{2}}\left( G\right) =\sum _{1\le i\le j\le n-1}m_{i,j}\left( G\right) e^{ij}, \end{aligned}$$ e M 2 G = ∑ 1 ≤ i ≤ j ≤ n - 1 m i , j G e ij , where $$m_{i,j}$$ 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 $$e^{M_{2}}$$ e M 2 . In this paper we show that the balanced double star tree has maximum value of $$e^{{\mathcal {M}}_{2}}$$ e M 2 .

Keywords: Vertex degree based topological indices; Exponential second Zagreb index; Maximal tree; 05C09; 05C92; 05C35 (search for similar items in EconPapers)
Date: 2021
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Citations: View citations in EconPapers (4)

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DOI: 10.1007/s10878-021-00696-3

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