摘要：The variable connectivity index, introduced by the chemist Milan Randić in the first quarter of 1990s, for a graph G is defined as ∑ v w ∈ E G d v + γ d w + γ − 1 / 2 , where γ is a non-negative real number and d w is the degree of a vertex w in G . We call this index as the variable Randić index and denote it by R v γ . In this paper, we show that the graph created from the star graph of order n by adding an edge has the minimum R v γ value among all unicyclic graphs of a fixed order n , for every n ≥ 4 and γ ≥ 0 .
