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Classical topological indices, such as Zagreb indices ( $$M_{1}$$ M 1 and $$M_2$$ M 2 ) and the well-studied eccentric connectivity index ( $$\xi ^{c}$$ ξ c ) directly or indirectly consider the total contribution of all edges in a graph. By considering the total degree sum of all non-adjacent vertex pairs in a graph, Ashrafi et al. (Discrete Appl Math 158:1571–1578, 2010) proposed...
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