On the maximum sigma index of k-cyclic graphs

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 Euv is an element of 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.(c) 2022 Elsevier B.V. All rights reserved.