摘要
The first and second Zagreb eccentricity indices of graph G are defined as:E1(G)=∑(vi)∈V(G)εG(vi)~2,E2(G)=∑(vivj)∈E(G)εG(vi)εG(vj)whereεG(vi)denotes the eccentricity of vertex vi in G.The eccentric complexity C(ec)(G)of G is the number of different eccentricities of vertices in G.In this paper we present some results on the comparison between E1(G)/n and E2(G)/m for any connected graphs G of order n with m edges,including general graphs and the graphs with given C(ec).Moreover,a Nordhaus-Gaddum type result C(ec)(G)+C(ec)(■)is determined with extremal graphs at which the upper and lower bounds are attained respectively.
The first and second Zagreb eccentricity indices of graph G are defined as:E1（G）=∑vi∈V（G）εG（vi）2,E2（G）=∑vivj∈E（G）εG（vi）εG（vj） where εG（vi） denotes the eccentricity of vertex vi in G.The eccentric complexity Cec（G） of G is the number of different eccentricities of vertices in G.In this paper we present some results on the comparison between E1（G）/n and E2（G）/m for any connected graphs G of order n with m edges,including general graphs and the graphs with given Cec.Moreover,a Nordhaus-Gaddum type result Cec（G）+Cec（■） is determined with extremal graphs at which the upper and lower bounds are attained respectively.
基金
Supported by NNSF of China(Grant No.11671202)
Sungkyun research fund,Sungkyunkwan University,2017
National Research Foundation funded by the Korean government(Grant No.2017R1D1A1B03028642)
