Structure and substructure connectivity of circulant graphs and hypercubes. Issue 1 (19th August 2020)

• Record Type: Journal Article
• Authors: Tamizh Chelvam, T.; Sivagami, M.
• Is Part Of: Arab journal of mathematical sciences. Volume 27:Issue 1(2021)
• Page Start: 94
• Page End: 103
• Publication Date: 2020-08-19
• Subjects: Structure connectivity -- Substructure connectivity -- Circulant graph -- Hypercube; 05C25 -- 05C40
• DOI: 10.1016/j.ajmsc.2019.10.001
• Languages: English
• ISSNs: 1319-5166

Abstract

Abstract : 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 = { H 1 ′, H 2 ′, …, H m ′ } 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 κ s ( G ; H ), is the minimum cardinality of a minimal set of subgraphs F = { J 1 ′, J 2 ′, …, J m ′ } in G, such that every J i ′ ∈ 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 ≤ ⌊ n 2 ⌋ and the hypercube Q n for some connected subgraphs H .