Further axiomatizations of Egghe's g-index

•We provide three axiomatic characterizations of Egghe's g-index.•Axioms T1, T2, and TA characterize a class of indexes including the g-index.•By adding SM and CC, the g-index is characterized.•CC can be dropped if adding IMC+ or strengthening SM and adding IMC.•Axioms other than T1 and T2 are newly introduced.

We provide three axiomatic characterizations of Egghe's g-index, which measures a researcher's scientific output based on the number of papers the researcher has published and the number of citations of each of the researcher's papers. We formulate six new axioms for indexes, namely, tail independence (TA), square monotonicity (SM), the cap condition (CC), strong square monotonicity (SSM), increasing marginal citations (IMC), and increasing marginal citations+ (IMC+). Along with the two well-known axioms T1 and T2 (Woeginger, 2008a), the g-index is characterized by (i) T1, T2, TA, SM, and CC, (ii) T1, T2, TA, SSM, and IMC, and (iii) T1, TA, SM, and IMC+. Two out of three characterizations are obtained by adding axioms to our new characterization of the class of indexes satisfying T1, T2, and TA, which are defined as generalizations of the g-index. Thus, the remaining four axioms in our first and second characterizations—SM, CC, SSM, and IMC—distinguish the original g-index from other related indexes in the class. Furthermore, the independence of our axioms and that of Woeginger's study is shown.