Z3-connectivity in Abelian Cayley graphs

Hao Li, Ping Li, Mingquan Zhan, Taoye Zhang, Ju Zhou

Research output: Contribution to journalArticle

Abstract

Let G be a 2-edge-connected undirected graph, A be an (additive) Abelian group and A = A - {0}. A graph G is A-connected if G has an orientation G such that for every map b : V(G) → A satisfying v V(G) b(v) = 0, there is a function f : E(G) → Asuch that for each vertex v V(G), the total amount of f -values on the edges directed out from v minus the total amount of f -values on the edges directed into v equals b(v). Jaeger et al. [F. Jaeger, N. Linial, C. Payan, M. Tarsi, Group connectivity of graphs-a nonhomogeneous analogue of nowhere-zero flow properties, J. Combinatorial Theory, Series B 56 (1992) 165-182] conjectured that every 5-edge-connected graph G is Z 3-connected, where Z3 is the cyclic group of order 3. In this paper we prove that every connected Cayley graph G of degree at least 5 on an Abelian group is Z3-connected.

Original languageEnglish (US)
Pages (from-to)1666-1676
Number of pages11
JournalDiscrete Mathematics
Volume313
Issue number16
DOIs
Publication statusPublished - Jan 1 2013

    Fingerprint

All Science Journal Classification (ASJC) codes

  • Theoretical Computer Science
  • Discrete Mathematics and Combinatorics

Cite this