Decomposition of augmented cubes into regular connected pancyclic subgraphs.

In this paper, we consider the problem of decomposing the augmented cube A Q n into two spanning, regular, connected and pancyclic subgraphs. We prove that for n ≥ 4 and 2 n − 1 = n 1 + n 2 with n 1 , n 2 ≥ 2 , A Q n can be decomposed into two spanning subgraphs H 1 and H 2 such that H i is n i -regular and n i -connected for i = 1 , 2. Moreover, H i is 4-pancyclic if n i ≥ 3. • In this paper we have given a decomposition of Augmented cube A Q n. • Decomposition gives us two spanning regular connected pancyclic subgraphs of A Q n. • Degrees of subgraphs are based on given 2-partition of 2 n − 1 which is the degree of A Q n . • They are optimal with respect to connectivity and cycle embedding. [ABSTRACT FROM AUTHOR]