Atoms of cyclic edge connectivity in regular graphs

Jin-Xin Zhou ()
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Jin-Xin Zhou: Beijing Jiaotong University

Journal of Combinatorial Optimization, 2016, vol. 31, issue 1, No 25, 382-395

Abstract: Abstract A cyclic edge-cut of a connected graph $$G$$ G is an edge set, the removal of which separates two cycles. If $$G$$ G has a cyclic edge-cut, then it is called cyclically separable. For a cyclically separable graph $$G$$ G , the cyclic edge connectivity of a graph $$G$$ G , denoted by $$\lambda _c(G)$$ λ c ( G ) , is the minimum cardinality over all cyclic edge cuts. Let $$X$$ X be a non-empty proper subset of $$V(G)$$ V ( G ) . If $$[X,\overline{X}]=\{xy\in E(G)\ |\ x\in X, y\in \overline{X}\}$$ [ X , X ¯ ] = { x y ∈ E ( G ) | x ∈ X , y ∈ X ¯ } is a minimum cyclic edge cut of $$G$$ G , then $$X$$ X is called a $$\lambda _c$$ λ c -fragment of $$G$$ G . A $$\lambda _c$$ λ c -fragment with minimum cardinality is called a $$\lambda _c$$ λ c -atom. Let $$G$$ G be a $$k (k\ge 3)$$ k ( k ≥ 3 ) -regular cyclically separable graph with $$\lambda _c(G)

Keywords: Cyclic edge connectivity; $$\lambda _c$$ λ c -atom; Edge-transitive graph; Vertex-transitive graph (search for similar items in EconPapers)
Date: 2016
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DOI: 10.1007/s10878-014-9759-4

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