Algorithm: as Construction of Cayley Graph which Embedded any Graph

Abstract

C.Delorme gave a proposition of construction of vertex-transitive graph. For this there is a group G and a subgroup H, and a subset A of G. the graph [G,H,A]are constructed. The vertices of graph are the parts of G of the forms xH , their number is the index of H in G.

The adjacent of xH are xah where a ЄA when H is reduced to an neuter element of the group. Cayley graph is found and it is associated to group G and the part A .

If gЄG , then xHègxH is an automorphism Nihad M. [3] found that there exist an Extension which in (n-1) monomorphic , which contains any binary relation , then Cayley graph is vertex transitive so (n-1) – monomorphic. In this work it is found that an Algorithm as construction Cayley graph which embedded any binary relation, and this Extension perhaps is finite or infinite.