TY - JOUR

T1 - Z3-connectivity in Abelian Cayley graphs

AU - Li, Hao

AU - Li, Ping

AU - Zhan, Mingquan

AU - Zhang, Taoye

AU - Zhou, Ju

N1 - Funding Information:
This work is supported by the Basic Research funds in Renmin University of China from the central government (No. 12XNLF02 ), Fundamental Research Funds for the Central Universities ( 2013JBM090 ).

PY - 2013

Y1 - 2013

N2 - 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.

AB - 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.

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U2 - 10.1016/j.disc.2013.04.008

DO - 10.1016/j.disc.2013.04.008

M3 - Article

AN - SCOPUS:84884815271

VL - 313

SP - 1666

EP - 1676

JO - Discrete Mathematics

JF - Discrete Mathematics

SN - 0012-365X

IS - 16

ER -