Some properties of the Zagreb eccentricity indices

Kinkar Ch. Das, Dae-Won Lee, Ante Graovac

Abstract


The concept of Zagreb eccentricity (E1 and E2) indices was introduced in the chemical graph theory very recently . The first Zagreb eccentricity (E1) and the second Zagreb eccentricity (E2) indices of a graph G are defined as

E1 = E1(G) = ∑vi ∈ V(G) ei2

and

E2 = E2(G) = ∑vivj ∈ E(G) ei ⋅ ej ,

where E(G) is the edge set and ei is the eccentricity of the vertex vi in G. In this paper we give some lower and upper bounds on the first Zagreb eccentricity and the second Zagreb eccentricity indices of trees and graphs, and also characterize the extremal graphs.


Keywords


Graph, first Zagreb eccentricity index, second Zagreb eccentricity index, diameter, eccentricity.

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DOI: https://doi.org/10.26493/1855-3974.237.48a

ISSN: 1855-3974

Issues from Vol 6, No 1 onward are partially supported by the Slovenian Research Agency from the Call for co-financing of scientific periodical publications