Structure and substructure connectivity of circulant graphs and hypercubes
Let H be a connected subgraph of a connected graph G. The H-structure connectivity of the graph G, denoted by κ(G;H), is the minimum cardinality of a minimal set of subgraphs F={H1′,H2′,…,Hm′} in G, such that every H′i∈F is isomorphic to H and removal of F from G will disconnect G. The H-substructur...
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| Format: | Article |
| Language: | English |
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Emerald Publishing
2021-04-01
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| Series: | Arab Journal of Mathematical Sciences |
| Subjects: | |
| Online Access: | https://www.emerald.com/insight/content/doi/10.1016/j.ajmsc.2019.10.001/full/pdf |
| _version_ | 1797791634747817984 |
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| author | T. Tamizh Chelvam M. Sivagami |
| author_facet | T. Tamizh Chelvam M. Sivagami |
| author_sort | T. Tamizh Chelvam |
| collection | DOAJ |
| description | Let H be a connected subgraph of a connected graph G. The H-structure connectivity of the graph G, denoted by κ(G;H), is the minimum cardinality of a minimal set of subgraphs F={H1′,H2′,…,Hm′} in G, such that every H′i∈F is isomorphic to H and removal of F from G will disconnect G. The H-substructure connectivity of the graph G, denoted by κs(G;H), is the minimum cardinality of a minimal set of subgraphs F={J1′,J2′,…,Jm′} in G, such that every Ji′∈F is a connected subgraph of H and removal of F from G will disconnect G. In this paper, we provide the H-structure and the H-substructure connectivity of the circulant graph Cir(n,Ω) where Ω={1,…,k,n−k,…,n−1},1≤k≤⌊n2⌋ and the hypercube Qn for some connected subgraphs H. |
| first_indexed | 2024-03-13T02:22:37Z |
| format | Article |
| id | doaj.art-fffa2446e654428f8eaccc4ac25be033 |
| institution | Directory Open Access Journal |
| issn | 1319-5166 2588-9214 |
| language | English |
| last_indexed | 2024-03-13T02:22:37Z |
| publishDate | 2021-04-01 |
| publisher | Emerald Publishing |
| record_format | Article |
| series | Arab Journal of Mathematical Sciences |
| spelling | doaj.art-fffa2446e654428f8eaccc4ac25be0332023-06-30T09:18:58ZengEmerald PublishingArab Journal of Mathematical Sciences1319-51662588-92142021-04-012719410310.1016/j.ajmsc.2019.10.001Structure and substructure connectivity of circulant graphs and hypercubesT. Tamizh Chelvam0M. Sivagami1Department of Mathematics, Manonmaniam Sundaranar University, Tirunelveli, IndiaDepartment of Mathematics, Manonmaniam Sundaranar University, Tirunelveli, IndiaLet H be a connected subgraph of a connected graph G. The H-structure connectivity of the graph G, denoted by κ(G;H), is the minimum cardinality of a minimal set of subgraphs F={H1′,H2′,…,Hm′} in G, such that every H′i∈F is isomorphic to H and removal of F from G will disconnect G. The H-substructure connectivity of the graph G, denoted by κs(G;H), is the minimum cardinality of a minimal set of subgraphs F={J1′,J2′,…,Jm′} in G, such that every Ji′∈F is a connected subgraph of H and removal of F from G will disconnect G. In this paper, we provide the H-structure and the H-substructure connectivity of the circulant graph Cir(n,Ω) where Ω={1,…,k,n−k,…,n−1},1≤k≤⌊n2⌋ and the hypercube Qn for some connected subgraphs H.https://www.emerald.com/insight/content/doi/10.1016/j.ajmsc.2019.10.001/full/pdfStructure connectivitySubstructure connectivityCirculant graphHypercube |
| spellingShingle | T. Tamizh Chelvam M. Sivagami Structure and substructure connectivity of circulant graphs and hypercubes Arab Journal of Mathematical Sciences Structure connectivity Substructure connectivity Circulant graph Hypercube |
| title | Structure and substructure connectivity of circulant graphs and hypercubes |
| title_full | Structure and substructure connectivity of circulant graphs and hypercubes |
| title_fullStr | Structure and substructure connectivity of circulant graphs and hypercubes |
| title_full_unstemmed | Structure and substructure connectivity of circulant graphs and hypercubes |
| title_short | Structure and substructure connectivity of circulant graphs and hypercubes |
| title_sort | structure and substructure connectivity of circulant graphs and hypercubes |
| topic | Structure connectivity Substructure connectivity Circulant graph Hypercube |
| url | https://www.emerald.com/insight/content/doi/10.1016/j.ajmsc.2019.10.001/full/pdf |
| work_keys_str_mv | AT ttamizhchelvam structureandsubstructureconnectivityofcirculantgraphsandhypercubes AT msivagami structureandsubstructureconnectivityofcirculantgraphsandhypercubes |