Investigation of General Power Sum-Connectivity Index for Some Classes of Extremal Graphs

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 , where and represent the degree of vertices and , respectively, and . A connected graph is called a - generalized quasi-tree if there exists a subset of cardinality such that the graph is a tree but for any subset of cardinality , the graph is not a tree. In this work, we find a sharp lower and some sharp upper bounds for this new sum-connectivity index.