International Journal of Mathematics and Mathematical Sciences
Volume 11 (1988), Issue 1, Pages 95-100

Homomorphisms and related contractions of graphs

Robert D. Girse and Richard A. Gillman

Department of Mathematics, Idaho State University, Pocatello 83209, ID, USA

Received 6 August 1985; Revised 16 July 1986

Copyright © 1988 Robert D. Girse and Richard A. Gillman. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.


For every homomorphism ϕ of a graph G there exists a contraction θϕ on G¯, the complement of G. Here we study the graph equation ϕ(G)=θϕ(G¯). In the course of our work we show that Hadwiger's Conjecture is true for every self-complementary graph.