TY - JOUR
T1 - Comparison of wiener index and zagreb eccentricity indices
AU - Xu, Kexiang
AU - Das, Kinkar Chandra
AU - Klavžar, Sandi
AU - Li, Huimin
N1 - Publisher Copyright:
© 2020 University of Kragujevac, Faculty of Science. All rights reserved.
PY - 2020
Y1 - 2020
N2 - The first and the second Zagreb eccentricity index of a graph G are defined as E1(G) = Pv∈V (G) εG(v)2 and E2(G) = Puv∈E(G) εG(u)εG(v), respectively, where εG(v) is the eccentricity of a vertex v. In this paper the invariants E1, E2, and the Wiener index are compared on graphs with diameter 2, on trees, on a newly introduced class of universally diametrical graphs, and on Cartesian product graphs. In particular, if the diameter of a tree T is not too big, then W(T) ≥ E2(T) holds, and if the diameter of T is large, then W(T) < E1(T) holds.
AB - The first and the second Zagreb eccentricity index of a graph G are defined as E1(G) = Pv∈V (G) εG(v)2 and E2(G) = Puv∈E(G) εG(u)εG(v), respectively, where εG(v) is the eccentricity of a vertex v. In this paper the invariants E1, E2, and the Wiener index are compared on graphs with diameter 2, on trees, on a newly introduced class of universally diametrical graphs, and on Cartesian product graphs. In particular, if the diameter of a tree T is not too big, then W(T) ≥ E2(T) holds, and if the diameter of T is large, then W(T) < E1(T) holds.
UR - https://www.scopus.com/pages/publications/85091787890
M3 - Article
AN - SCOPUS:85091787890
SN - 0340-6253
VL - 84
SP - 595
EP - 610
JO - Match
JF - Match
IS - 3
ER -