# DMGT

ISSN 1234-3099 (print version)

ISSN 2083-5892 (electronic version)

# IMPACT FACTOR 2019: 0.755

SCImago Journal Rank (SJR) 2019: 0.600

Rejection Rate (2018-2019): c. 84%

# Discussiones Mathematicae Graph Theory

Article in press

Authors:

H. Hua, H. Wang and I. Gutman

Title:

Comparing eccentricity-based graph invariants

Source:

Discussiones Mathematicae Graph Theory

Received: 2018-01-26, Revised: 2018-01-26, Accepted: 2018-08-18, https://doi.org/10.7151/dmgt.2171

Abstract:

The first and second Zagreb eccentricity indices ($EM_1$ and $EM_2$), 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 $\geq EM_1$ for any connected graph, whereas EDS $> EM_2$ for trees. Moreover, in the case of trees, $EM_1 \geq$ CEI, whereas $EM_2 >$ CEI for trees with at least three vertices. In addition, we compare EDS with $EM_2$, and compare $EM_1$, $EM_2$ with CEI for general connected graphs under some restricted conditions.

Keywords:

eccentricity (of vertex), Zagreb eccentricity index, eccentric distance sum, connective eccentricity index