Structure and substructure connectivity of folded divide-and-swap cube
Makaleler > Tam Makale · 2025
Yazarlar: Muhammed Türkmen, Canan Çiftçi, Gülnaz BORUZANLI EKİNCİ
The Journal of Supercomputing, Uluslararası, Wos, 2025, cilt 81
DOI: 10.1007/s11227-025-07100-5
Özet
Abstract Let $$ {\mathcal {H}} $$ H be a connected subgraph of a graph G. The $${\mathcal {H}}$$ H -structure connectivity of G, denoted by $$ \kappa (G;{\mathcal {H}}) $$ κ ( G ; H ) , is the minimum cardinality of a set of connected subgraphs in G, whose removal either disconnects G or reduces it to a trivial graph, where each element in the set is isomorphic to $$ {\mathcal {H}} $$ H . The $${\mathcal {H}}$$ H -substructure connectivity of G, denoted by $$ \kappa ^s(G;{\mathcal {H}}) $$ κ s ( G ; H ) , is the minimum cardinality of a set of connected subgraphs in G, whose removal either disconnects G or reduces it to a trivial graph, where each element in the set is isomorphic to a connected subgraph of $$ {\mathcal {H}} $$ H . In this paper, we investigate the $$ {\mathcal {H}} $$ H -structure connectivity and $$ {\mathcal {H}} $$ H -substructure connectivity of folded divide-and-swap cube $$ FDSC_n $$ F D S C n for $$ {\mathcal {H}}\in \{K_1, K_{1,1}, K_{1,m} \text (2\le m \le d+2) \} $$ H ∈ { K 1 , K 1 , 1 , K 1 , m ( 2 ≤ m ≤ d + 2 ) } where $$ n=2^d $$ n = 2 d . We show that $$\kappa (FDSC_n;K_1)=\kappa ^s(FDSC_n;K_1)=d+2$$ κ ( F D S C n ; K 1 ) = κ s ( F D S C n ; K 1 ) = d + 2 , $$\kappa (FDSC_n;K_{1,1})=\kappa ^s(FDSC_n;K_{1,1})=d+1 $$ κ ( F D