Original scientific paper

https://doi.org/10.5562/cca1801

On Zagreb Eccentricity Indices

Rundan Xing ; Department of Mathematics, South China Normal University, Guangzhou 510631, China
Bo Zhou orcid.org/0000-0001-7321-9554 ; Department of Mathematics, South China Normal University, Guangzhou 510631, China
Nenad Trinajstić ; The Rugjer Bošković Institute, P. O. Box 180, HR-10 002 Zagreb, Croatia

Abstract

Zagreb eccentricity indices were proposed analogously to Zagreb indices already known and
used for almost forty years. For a connected graph, the first Zagreb eccentricity index is defined as the
sum of the squares of the eccentricities of the vertices, and the second Zagreb eccentricity index is defined
as the sum of the products of the eccentricities of pairs of adjacent vertices. We report mathematical properties,
especially lower and upper bounds of trees and general graphs in terms of graph invariants and the
corresponding extremal graphs, Nordhaus-Gaddum-type results, and the ordering of trees with small and
large Zagreb eccentricity indices. (doi: 10.5562/cca1801)

Keywords

Zagreb indices; Zagreb eccentricity indices; lower and upper bounds; graph invariants; trees; general graphs

Hrčak ID:

75058

URI

https://hrcak.srce.hr/75058

Publication date:

20.12.2011.

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