For an even integer n 2 and 1 blog2 nc, a Knödel graph W;n is a -regular bipartite graph of even order n, with vertices (i; j), for i = 1; 2 and 0 j n=2 1, where for every j, 0 j n=2 1, there is an edge between vertex (1; j) and every vertex (2; (j + 2k 1) mod (n/2)), for k = 0; 1; ; 1. In this note, we express and prove some of the adjacency conditions in the Knödel graphs and we will show that every Knödel graph is a K2;3-free graph.
