A note on graphically summable sequences

AbstractThe 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.