Abstract
The graphs with diameter equal to n − c , for 1 ⩽ c ⩽ 4 , which attain the minimum value with respect to the Harary index are being considered. Additionally, the sharp lower bound on Harary index of connected graphs with independence number equal to n − c , for 1 ⩽ c ⩽ 4 is derived. The extremal graphs are also characterized.
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