# The Existence of (K2 × K6)-Designs

Research paper by Chengmin Wang, Charles J. Colbourn

Indexed on: 12 May '12Published on: 12 May '12Published in: Graphs and Combinatorics

#### Abstract

Direct and recursive constructions are established for graph designs for K2 × K6 grid-blocks. Using these, the existence of graph designs of index one in which the blocks are K2 × K6 grid-blocks is completely determined: A (K2 × K6)-design of order v exists if and only if $${v\equiv1\pmod{72}}$$.