Bounds and Inequalities Relating h-Index, g-Index, e-Index and Generalized Impact Factor: An Improvement over Existing Models

In this paper, we describe some bounds and inequalities relating h-index, g-index, e-index, and generalized impact factor. We derive the bounds and inequalities relating these indexing parameters from their basic definitions and without assuming any continuous model to be followed by any of them. We verify the theorems using citation data for five Price Medalists. We observe that the lower bound for h-index given by Theorem 2, h = Omega (left perpendicular g - g/e(2) right perpendicular), g >= 1, comes out to be more accurate as compared to Schubert-Glanzel relation h proportional to C2/3P1/3 for a proportionality constant of 1, where C is the number of citations and P is the number of papers referenced. Also, the values of h-index obtained using Theorem 2 outperform those obtained using Egghe-Liang-Rousseau power law model for the given citation data of Price Medalists. Further, we computed the values of upper bound on g-index given by Theorem 3, g <= (h+e), where e denotes the value of e-index. We observe that the upper bound on g-index given by Theorem 3 is reasonably tight for the given citation record of Price Medalists.