The Euclidean dimension of the join of two cycles

Abstract

The Euclidean dimension of a graph G is the smallest integer p such that the vertices of G can be represented by points in the Euclidean space R p with two points being 1 unit distance apart if and only if they represent adjacent vertices. We show that dim ( C m + C n ) = 5 except that dim ( C 4 + C 4 ) = 4 , dim ( C 5 + C 5 ) = 4 , and dim ( C 6 + C 6 ) = 6 .