A note on graphically summable sequences

Abstract

The notion of Jaco-type graphs has been introduced recently as the graphical embodiments of well-defined integer sequences. For a Jaco-type graph, the vertex out-degree d⁺(v) is well-defined. It is noted that for a given out-degree integer sequence, a specific in-degree sequence results. Graphically summable sequences are a pair of integer sequences, such that for a given out-degree sequence, say s₁⁺, a specific in-degree sequence, say s₂^-, inevitably results. In this paper, we also report on the second and third known combinatorial interpretation of the Hofstadter G-sequence.

Keywords:

• Jaco-type graph
• Fibonaccian Jaco-type graph
• modular Jaco-type graph
• Hofstadter G-sequence

Mathematics Subject Classification:

• 05C07
• 05C38
• 05C75
• 05C85