Minimum general sum-connectivity index of trees and unicyclic graphs having a given matching number

In this paper it is shown that the characterizations of trees and unicyclic graphs having a given matching number and minimum connectivity index χ−1∕2, proposed by Du et al. (2010) remain valid for general connectivity index χα if −1≤α<0 for trees and −0.585≤α<0 for unicyclic graphs. The extremal result for trees having a given matching number is also true for the harmonic index H, since for any graph H(G)=2χ−1(G) holds.