Comparing eccentricity-based graph invariants

Abstract

© 2020 Sciendo. All rights reserved. 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 con- nected graph, whereas EDS > EM2 for trees. Moreover, in the case of trees, EM1 ≤ CEI, whereas EM2 > 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.