Abstract
For a graph G=(V,E), the exponential second Zagreb index is defined as eM2(G)=∑uv∈Eed(u)d(v), where d(v) is the degree of vertex v∈V. Recently, Eliasi (2022) posed a conjecture about (n,m)-graphs with maximum eM2 when n≤m≤2n−3. In this paper, we show that this conjecture is true. Furthermore, we determine the graphs with maximum eM2 among all (n,m)-graphs when 2n−3<m.
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