This analysis uncovers the maximum value of the multiplicative sum zagreb index in molecular trees, suggesting implications for graph structures.
The multiplicative sum Zagreb index of a graph G is defined as the product of the sum of the degrees of adjacent vertices of G . A molecular tree is an acyclic connected graph with maximum degree at most 4. A vertex in a molecular tree with degree 3 or 4 is referred to as a branching vertex. In this paper, we consider the class of all molecular trees of fixed order and with a given number of branching vertices and study the members of this class with the maximum value of the multiplicative sum Zagreb index.
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Noureen et al. (2025) studied this question.
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