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Remoteness and distance eigenvalues of a graph.
- Source :
-
Discrete Applied Mathematics . Dec2016, Vol. 215, p218-224. 7p. - Publication Year :
- 2016
-
Abstract
- Let G be a connected graph of order n with diameter d . Remoteness ρ of G is the maximum average distance from a vertex to all others and ∂ 1 ≥ ⋯ ≥ ∂ n are the distance eigenvalues of G . Aouchiche and Hansen (0000), Aouchiche and Hansen conjectured that ρ + ∂ 3 > 0 when d ≥ 3 and ρ + ∂ ⌊ 7 d 8 ⌋ > 0 . In this paper, we confirm these two conjectures. Furthermore, we give lower bounds on ∂ n + ρ and ∂ 1 − ρ when G ≇ K n and the extremal graphs are characterized. [ABSTRACT FROM AUTHOR]
- Subjects :
- *EIGENVALUES
*GRAPH theory
*GRAPH connectivity
*ARITHMETIC mean
*MATHEMATICAL bounds
Subjects
Details
- Language :
- English
- ISSN :
- 0166218X
- Volume :
- 215
- Database :
- Academic Search Index
- Journal :
- Discrete Applied Mathematics
- Publication Type :
- Academic Journal
- Accession number :
- 118311624
- Full Text :
- https://doi.org/10.1016/j.dam.2016.07.018