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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  Y α G = ∑ u v ∈ E G d u d u + d v d v α , where  d u and  d v 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  V k ⊂ V G of cardinality  k such that the graph  G − V k is a tree but for any subset  V k − 1 ⊂ V G of cardinality  k − 1 , the graph  G − V k − 1 is not a tree. In this work, we find a sharp lower and some sharp upper bounds for this new sum-connectivity index.

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