Conditional connectivity of Cayley graphs generated by transposition trees

A kind of conditional fault tolerance of -star graphs

“…Later, Cheng and Lipták [7], and Yang et al [20] determined κ 1 and κ 2 of Cayley graphs generated by transposition trees independently which is a supplement of Wan and Zhang's result. Lower bounds for κ k in m-ary n-dimensional hypercube were studied by Wu and Guo [19].…”

A kind of conditional connectivity of transposition networks generated by k-trees

“…We list the following known results due to Wang and Zhang. Cheng and Lipták [8], and Yang and Meng [26] generalized the result above to the Cayley graphs generated by transposition generating trees. 22]).…”

“…For convenience, we assume n is the last vertex added on G(T ), that is, the degree of n in G(T ) is k. And we call a vertex of degree k in T k,n is a leaf. Moreover, we assume k ≥ 2, as the case for k = 1 has been considered in [8,26]. One most important property of transposition networks is the hierarchical structure, which is particularly useful in our inductive arguments.…”

Embedded connectivity of recursive networks

“…However, when Lemma 1.1 is used, they assume an incorrect conclusion: λ 2 (B n ) = 6(n−3) (see Lemma 4.6 in [13]). In fact, λ 2 (B n ) = 4(n − 3) for n ≥ 4 (see [11]). It follows that Yang et al's proof is not correct.…”