EXTREMAL k-GENERALIZED QUASI TREES FOR GENERAL SUM-CONNECTIVITY INDEX

For a simple graph G, the general sum-connectivity index is defined as chi(alpha)(G) = Sigma(uv is an element of E(G)) (d(u) + d(v))(alpha), where d(u) is the degree of the vertex u and alpha not equal 0 is a real number. The k-generalized quasi tree is a connected graph G with a subset V-k subset of V (G), where vertical bar V-k vertical bar = k such that G - V-k is a tree, but for any subset Vk-1 subset of V (G) with cardinality k - 1, G - Vk-1 is not a tree. In this paper, we have determined sharp upper and lower bounds of the general sum-connectivity index for alpha >= 1. The corresponding extremal k-generalized quasi trees are also characterized in each case.