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- W2889968425 abstract "For a connected graph G = ( V , E ) , an edge set S ⊆ E is a k -restricted edge cut if G − S is disconnected and every component of G − S has at least k vertices. The k -restricted edge connectivity of G , denoted by λ k ( G ) , is defined as the cardinality of a minimum k -restricted edge cut. Let ξ k ( G ) = min { | [ X , X ̄ ] | : | X | = k , G [ X ] is connected } , where X ̄ = V ∖ X . G is maximally k -restricted edge connected ( λ k -optimal for short) if λ k ( G ) = ξ k ( G ) . The k -restricted edge connectivity is more refined network reliability index than the edge connectivity. In this paper, for graph G with girth g ≥ 2 k + 1 and minimum degree δ ≥ k , we present a lower bound on the cardinality of λ k -atoms of G when λ k ( G ) < ξ k ( G ) . Moreover, we give some sufficient conditions for graphs with girth g to be λ k -optimal." @default.
- W2889968425 created "2018-09-27" @default.
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- W2889968425 date "2019-02-01" @default.
- W2889968425 modified "2023-09-28" @default.
- W2889968425 title "Sufficient conditions for graphs with girth <mml:math xmlns:mml=http://www.w3.org/1998/Math/MathML id=mml3 display=inline overflow=scroll altimg=si3.gif><mml:mi>g</mml:mi></mml:math> to be maximally <mml:math xmlns:mml=http://www.w3.org/1998/Math/MathML id=mml4 display=inline overflow=scroll altimg=si4.gif><mml:mi>k</mml:mi></mml:math>-restricted edge connected" @default.
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- W2889968425 doi "https://doi.org/10.1016/j.dam.2018.07.027" @default.
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