Reliability analyses of regular graphs based on edge-structure connectivity

Let G be a graph and F be a connected subgraph of G except for K 1 . Let F = { F 1 , F 2 , ... , F k } be a set of subgraphs of G such that each member of F is isomorphic to F . The F -(disjoint) -structure edge -connectivity is the minimum cardinality of F such that E ( F )'s removal will disconnect G . If every member of F is isomorphic to a connected subgraph of F , then F -(disjoint) -substructure edge -connectivity is defined similarly. In this paper, we determine the star -(disjoint) -substructure edge -connectivity and star -structure edge -connectivity of an n -regular graph G , and give an upper bound on the star -disjoint -structure edge -connectivity of an n -regular graph G . We derive the F -(disjoint) -substructure edge -connectivity of hypercube-like graphs HL n and Cayley graphs generated by transposition trees Gamma n (except for star graphs S n ) for F being C 4 and P 4 , and show a lower bound on the F -(disjoint) -structure edge -connectivity of HL n and Gamma n (except for S n ) for F being C 4 and P 4 . As applications, we determine the F(disjoint) -structure edge -connectivity of crossed cubes CQ n and bubble -sort graphs B n for F being C 4 and P 4 , respectively. Furthermore, we obtain the F -(disjoint)-(sub)structure edge -connectivity of S n for F being C 6 and P 6 . (c) 2024 Elsevier B.V. All rights are reserved, including those for text and data mining, AI training, and similar technologies.