1. Comparison and Extremal Results on Three Eccentricity-based Invariants of Graphs.
- Author
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Xu, Ke Xiang, Das, Kinkar Chandra, and Gu, Xiao Qian
- Subjects
GEOMETRIC vertices ,GRAPH connectivity - Abstract
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 ε
G (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]- Published
- 2020
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