Authors:
I. Gutman, H. Hua, H. Wang
Title:
Comparing eccentricity-based graph invariants
Source:
Discussiones Mathematicae Graph Theory
Received 26.01.2018, Revised 26.01.2018, Accepted 18.08.2018, doi: 10.7151/dmgt.2171

Abstract:
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 > 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.
Keywords:
eccentricity (of vertex), Zagreb eccentricity index, eccentric distance sum, connective eccentricity index

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