International Journal of Mathematics and Mathematical Sciences 
Volume 9 (1986), Issue 1, Pages 193-195
doi:10.1155/S0161171286000224

Homomorphisms of complete n-partite graphs

Robert D. Girse

Department of Mathematics, Idaho State University, Pocatello 83209–0009, Idaho, USA

Received 24 January 1985; Revised 10 April 1985

Abstract

It is shown that for every homomorphism ϕ of a graph G there exists a contraction θϕ on G¯, the complement of G, such that ϕ(G)¯=θϕ(G¯) if and only if G is a complete n-partite graph.