In this work, we introduce a new topological index called a general power sum-connectivity index and we discuss this graph invariant for some classes of extremal graphs. This index is defined by YαG=∑uv∈EGdudu+dvdvα, where du and dv represent the degree of vertices u and v, respectively, and α≥1. A connected graph G is called a k-generalized quasi-tree if there exists a subset Vk⊂VG of cardinality k such that the graph G−Vk is a tree but for any subset Vk−1⊂VG of cardinality k−1, the graph G−Vk−1 is not a tree. In this work, we find a sharp lower and some sharp upper bounds for this new sum-connectivity index.
