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引用次数: 0
摘要
摘要:如果存在一个图H满足SB(H)≌G，则称图G为半分裂块图。本文基于G的顶点集的划分，建立了半分裂块图的一个刻画，研究了SB(G)的顶点(边)连通性和p边连通性。对于所有1 < a < b的整数a, b，证明了k (G) = a, k (SB(G)) = b和λ (G) = a， λ (SB(G)) = b的图G的存在性。得到了κ(SB(G)) = κ(G)的图的表征和κ(SB(G)) = λ (SB(G))的图的必要条件。
On connectivity of the semi-splitting block graph of a graph
Abstract A graph G is said to be a semi-splitting block graph if there exists a graph H such that SB(H) ≌ G. This paper establishes a characterisation of semi-splitting block graphs based on the partition of the vertex set of G. The vertex (edge) connectivity and p-connectedness (p-edge connectedness) of SB(G) are examined. For all integers a, b with 1 < a < b, the existence of the graph G for which κ (G) = a, κ (SB(G)) = b and λ (G) = a, λ (SB(G)) = b are proved independently. The characterization of graphs with κ(SB(G)) = κ (G) and a necessary condition for graphs with κ (SB(G)) = λ (SB(G)) are achieved.
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