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- W4313201771 abstract "Let G be a simple graph. A vertex-subset (edge-subset) D⊆V(G) (D⊆E(G)) is called an m-restricted vertex-cut (edge-cut) of G if G−D is disconnected and δ(G−D)≥m. The m-restricted (edge) connectivity of G, denoted by κm(G) (λm(G)), is the size of a smallest m-restricted vertex-cut (edge-cut). Let B be the symmetric group on [n]={1,2,…,n} and X be a set of transposition of B. Let G(X) be the generating graph with V(G(X))=[n] and E(G(X))={(c,d)∣(c,d)∈X}. If G(X) is isomorphic to a tree, the Cayley graph Cay(B,X), denoted by Γn, is the so called Cayley graph generated by transposition tree. Specially, if G(X) is isomorphic to a path, then Γn is the well-known bubble sort graph Bn; if G(X) is isomorphic to a star, then Γn is star graph Sn. In this work, we investigate m-restricted (edge) connectivity of Cayley graph Γn, whose generating graph G(X) has maximum matching number h. When 1≤m≤h, we show that the m-restricted (edge) connectivity of Γn is κm(Γn)=2m(n−1−m) (resp., λm(Γn)=2m(n−1−m))." @default.
- W4313201771 created "2023-01-06" @default.
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- W4313201771 date "2023-03-01" @default.
- W4313201771 modified "2023-10-01" @default.
- W4313201771 title "Restricted connectivity of Cayley graph generated by transposition trees" @default.
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- W4313201771 doi "https://doi.org/10.1016/j.dam.2022.11.012" @default.
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