Search

The first and second Zagreb eccentricity indices of graph G are defined as: E 1 (G) = ∑ v i ∈ V (G) ε G ( v i ) 2 , E 2 (G) = ∑ v i v j ∈ E (G) ε G ( v i ) ε G ( v j ) where εG(υi) denotes the eccentricity of vertex υi 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 E 1 (G) n and E 2 (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(Ḡ) is determined with extremal graphs at which the upper and lower bounds are attained respectively. [ABSTRACT FROM AUTHOR]