The pull-back [g.sup.*]: [N.sup.1.sub.C](Y) [equivalent] [N.sup.1.sub.C](Y) induces an automorphism
Some preliminary results about monoidal Hom-algebras with Frobenius property have been studied, such as when finite dimensional monoidal Hom-Hopf algebras are Frobenius associated with integral spaces , the structures of separable and Frobenius monoidal Hom-algebras related to the Hom-Frobenius-separability equation, as well as the Nakayama automorphism
of Frobenius monoidal Hom-algebras , and so on.
Since the Dunkl transform is an automorphism
of S([R.sup.d]), the space is a closed linear subspace of S([R.sup.d]).
This endomorphism is an automorphism
if and only if k and 5 are coprime.
Similarly we can define [mathematical expression not reproducible] is the identity automorphism
of [mathematical expression not reproducible].
Next we would determine the automorphism
group of the digraph G(H, f).
Let [GAMMA] be a graph with automorphism
Bhutani, "On automorphisms
of fuzzy graphs," Pattern Recognition Letters, vol.
(i) If [mathematical expression not reproducible] is a finite field, then [mathematical expression not reproducible] is a cyclic group of order m and is generated by Frobenius automorphism
A topological index is a numeric quantity associated with a graph which characterize the topology of graph and is invariant under graph automorphism
. There are some major classes of topological indices such as distance based topological indices, degree based topological indices and counting related polynomials and indices of graphs.