Hamiltonian decomposition of generalized recursive circulant graphs

• GRC graphs have more flexible structures than recursive circulant graphs.
• We construct edge-disjoint Hamiltonian cycles of GRC graphs.
• We prove that some of the GRC graphs are Hamiltonian decomposable.

In 2012, Tang et al. [9] proposed a new class of graphs called generalized recursive circulant (GRC) graphs, which is an extension of recursive circulant graphs. GRC graphs have a more flexible structure than recursive circulant graphs, while retaining their attractive properties, such as degree, connectivity, diameter, and routing algorithm. In this paper, the Hamiltonian decomposition of some GRC graphs is discussed.