The Atom-bond-connectivity index ABC of a graph G is determined by d_i and d_j. In this paper, sharp results for the general which has chemical applications are found using different methods. These new inex investigated in terms its edges, vertices degrees. particular, some relations obtained involving topological indices; Randic index, Zagreb Harmonic Narumi-Katayama index. Indeed, improved he...

A connected graph G is said to be k-connected if it has more than k vertices and remains whenever fewer are deleted. In this paper, for a with sufficiently large order, we present tight sufficient condition fixed minimum degree based on the Q-index. Our result can viewed as spectral counterpart of corresponding Dirac-type condition.