TY - JOUR
T1 - Small-diameter Cayley Graphs for Finite Simple Groups
AU - Babai, L.
AU - Kantor, W. M.
AU - Lubotsky, A.
PY - 1989
Y1 - 1989
N2 - Let S be a subset generating a finite group G. The corresponding Cayley graph G(G, S) has the elements of G as vertices and the pairs {g, sg}, g ∈ G, s ∈ S, as edges. The diameter of G(G, S) is the smallest integer d such that every element of G can be expressed as a word of length ⩿d using elements from S ∪ S−1. A simple count of words shows that d ⩾ log2 ❘s❘ (❘G❘). We prove that there is a constant C such that every nonabelian finite simple group has a set S of at most 7 generators for which the diameter of G(G, S) is at most C log ❘G❘.
AB - Let S be a subset generating a finite group G. The corresponding Cayley graph G(G, S) has the elements of G as vertices and the pairs {g, sg}, g ∈ G, s ∈ S, as edges. The diameter of G(G, S) is the smallest integer d such that every element of G can be expressed as a word of length ⩿d using elements from S ∪ S−1. A simple count of words shows that d ⩾ log2 ❘s❘ (❘G❘). We prove that there is a constant C such that every nonabelian finite simple group has a set S of at most 7 generators for which the diameter of G(G, S) is at most C log ❘G❘.
UR - https://www.scopus.com/pages/publications/85009806236
U2 - 10.1016/S0195-6698(89)80067-8
DO - 10.1016/S0195-6698(89)80067-8
M3 - ???researchoutput.researchoutputtypes.contributiontojournal.article???
AN - SCOPUS:85009806236
SN - 0195-6698
VL - 10
SP - 507
EP - 522
JO - European Journal of Combinatorics
JF - European Journal of Combinatorics
IS - 6
ER -