Some Upper Bounds on the First General Zagreb Index

The first general Zagreb index M(gamma)G or zeroth-order general Randic index of a graph G is defined as M-gamma (G)& nbsp; = sigma v epsilon V d(v)(e & nbsp;) nbsp;where gamma is any nonzero real number, d(v) is the degree of the vertex v and gamma=2 gives the classical first Zagreb index. The researchers investigated some sharp upper and lower bounds on zeroth-order general Randic index (for gamma < 0) in terms of connectivity, minimum degree, and independent number. In this paper, we put sharp upper bounds on the first general Zagreb index in terms of independent number, minimum degree, and connectivity for gamma. Furthermore, extremal graphs are also investigated which attained the upper bounds.