The diagram below displays the pairs of three-letter words. If you read the four letters around each four-vertex that have not yet been used, starting with the circled letter, and then order these tetragrams in the only way that makes sense, you get the message:
NOWR EADA ROUN DSIX THVE RTEX
Reading in a circle around the sixth four-vertex (i.e., the one you
found RTEX around) is the answer JAYHAWKS.