Geodesic
Comparing Eccentricity-Based Graph Invariants
Discussiones Mathematicae. Graph Theory, Tome 40 (2020) no. 4, pp. 1111-1125.

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The first and second Zagreb eccentricity indices (EM1 and EM2), the eccentric distance sum (EDS), and the connective eccentricity index (CEI) are all recently conceived eccentricity-based graph invariants, some of which found applications in chemistry. We prove that EDS ≥ EM1 for any connected graph, whereas EDS gt; EM2 for trees. Moreover, in the case of trees, EM1 ≥ CEI, whereas EM2 gt; CEI for trees with at least three vertices. In addition, we compare EDS with EM2, and compare EM1, EM2 with CEI for general connected graphs under some restricted conditions.
Keywords: eccentricity (of vertex), Zagreb eccentricity index, eccentric distance sum, connective eccentricity index 
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Hua, Hongbo; Wang, Hongzhuan; Gutman, Ivan. Comparing Eccentricity-Based Graph Invariants. Discussiones Mathematicae. Graph Theory, Tome 40 (2020) no. 4, pp. 1111-1125. http://geodesic.mathdoc.fr/item/DMGT_2020_40_4_a11/

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