Conditions for building generalized action graphs from sequences

Abstract: This paper explores the properties of directed graphs, termed generalized action graphs, which exhibit a strong connection to certain number sequences. Focusing on the structural and combinatorial aspects, we investigate the conditions under which specific sequences can generate generalized action graphs. Building upon prior research in this field, we analyze specific features of these graphs and how they correspond to patterns and properties in their sequences. These findings support a broader conclusion that establishes framework for identifying which sequences can produce generalized action graphs.