Full automorphism group of commuting and non-commuting graph of dihedral and symmetric groups

An automorphism of finite graph G is a permutation on its vertex set that conserves adjacency. The set of all automorphism of G is a group under composition of function. This group is called the full automorphism group of G. Study on the full automorphism group is an interesting topic because most graphs have only the trivial automorphism and many special graphs have many automorphisms. One of the special graphs is graph that associated with group. The result of this paper is the full automorphism groups of commuting and non-commuting graph of non-abelian finite group, especially on dihedral and symmetric groups, according to the choice of their subgroups

SMARANDACHE GEOMETRIES & MAP THEORY WITH APPLICATIONS (I)

Combinatorics is a powerful tool for dealing with relations among objectives mushroomed in the past century. However, an even more important work for mathematician is to apply combinatorics to other mathematics and other sciences beside just to find combinatorial behavior for objectives. In the past few years, works of this kind frequently appeared on journals for mathematics and theoretical physics for cosmos. The main purpose of this paper is to survey these thinking and ideas for mathematics and cosmological physics, such as those of multi-spaces, map geometries and combinatorial cosmoses, also the combinatorial conjecture for mathematics