Maximally edge-connected graphs and Zeroth-order general Randić index for α≤-1

Let G be a connected graph with order n , minimum degree δ = δ ( G ) and edge-connectivity λ = λ ( G ) . A graph G is maximally edge-connected if λ = δ . In this paper, we present two sufficient conditions for graphs to be maximally edge-connected, which generalize two results recently proved by P....

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Bibliographic Details
Published inJournal of combinatorial optimization Vol. 31; no. 1; pp. 182 - 195
Main Authors Su, Guifu, Xiong, Liming, Su, Xiaofeng, Li, Guojun
Format Journal Article
LanguageEnglish
Published New York Springer US 2016
Subjects
Combinatorics
Convex and Discrete Geometry
Mathematical Modeling and Industrial Mathematics
Mathematics
Mathematics and Statistics
Operations Research/Decision Theory
Optimization
Theory of Computation
Edge-connectivity
Maximally edge-connected
Zeroth-order general Randić index
Degree (of vertex)
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Summary:Let G be a connected graph with order n , minimum degree δ = δ ( G ) and edge-connectivity λ = λ ( G ) . A graph G is maximally edge-connected if λ = δ . In this paper, we present two sufficient conditions for graphs to be maximally edge-connected, which generalize two results recently proved by P. Dankelmann, A. Hellwig and L. Volkmann. The extremal graphs are also characterized.
ISSN:1382-6905
1573-2886
DOI:10.1007/s10878-014-9728-y