Some properties of the Zagreb eccentricity indices

Abstract

The concept of Zagreb eccentricity (E 1 and E 2 ) indices was introduced in the chemical graph theory very recently [5,12]. The first Zagreb eccentricity (E 1 ) and the second Zagreb eccentricity (E 2 ) indices of a graph G are defined aswhere E(G) is the edge set and e i is the eccentricity of the vertex v i 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.

The Second Multiplicative Zagreb Eccentricity Index of Circumcoronene Series of Benzenoid

“…For further results of the Zagreb eccentricity indices, we encourage the reader refer to [15][16][17][18][19][20][21][22][23][24].…”

Some Invariants of Jahangir Graphs

“…For details on these indices, we refer [31][32][33][34] to the readers. The Symmetric division index is defined as:…”

Sharp lower bounds for the Zagreb indices of unicyclic graphs

“…Their main properties were summarized in [4,7,13,19]. Some recent results on the Zagreb indices are reported in [4,5,[9][10][11][12][14][15][16][17][18][19][20]. [18] gave the unicyclic graphs with the first three smallest and largest M 1 .…”

“…These indices reflect the extent of branching of the molecular carbon-atom skeleton, and can thus be viewed as molecular structure descriptors [1] and [15]. Their main properties were summarized in [4,7,13,19]. Some recent results on the Zagreb indices are reported in [4,5,[9][10][11][12][14][15][16][17][18][19][20].…”