We found a match
Your institution may have access to this item. Find your institution then sign in to continue.
- Title
Tree Connectivities of Cayley Graphs on Abelian Groups with Small Degrees.
- Authors
Sun, Yuefang; Zhou, Sanming
- Abstract
The generalized k-connectivity $$\kappa _{k}(G)$$ and the generalized k-edge-connectivity $$\lambda _k(G)$$ of a graph G, also known as the tree connectivities, were introduced by Hager (J Comb Theory Ser B 38:179-189, 1985) and Li et al. (Discret Math Theor Comput Sci 14:43-54, 2012), respectively. In this paper, we study these invariants for Cayley graphs on Abelian groups with degree 3 or 4. When G is cubic, we prove $$\kappa _k(G) = \lambda _k(G) = 2$$ for $$3\le k\le 6$$ and $$\kappa _k(G) = \lambda _k(G) = 1$$ for $$7\le k\le n$$ . When G has degree 4, we obtain $$\kappa _{3}(G)=\lambda _3(G)=3$$ , $$\lambda _k(G) = 2$$ and $$\kappa _k(G)\le 2$$ for $$k\ge 8$$ , and $$\kappa _k(G) = 2$$ for $$k=n-1,n$$ .
- Subjects
TREE graphs; GRAPH connectivity; CAYLEY graphs; ABELIAN groups; MATHEMATICAL proofs
- Publication
Bulletin of the Malaysian Mathematical Sciences Society, 2016, Vol 39, Issue 4, p1673
- ISSN
0126-6705
- Publication type
Article
- DOI
10.1007/s40840-015-0147-8