Abstract
Let G be a graph with edge set E(G). Denote by dw the degree of a vertex w of G. The sigma index of G is defined as ∑uv∈E(G)(du−dv)2. A connected graph of order n and size n+k−1 is known as a connected k-cyclic graph. Abdo et al. (2018) characterized the graphs having the greatest sigma index over the family of all connected graphs of a fixed order. The primary goal of the present note is to determine the unique graph possessing the greatest sigma index from the class of all connected k-cyclic graphs of order n for every pair of fixed integers k and n satisfying 0≤k≤n−2.