On the Vertex In-Degrees of Certain Jaco-Type Graphs

TL;DR

This paper investigates the in-degree properties of Fibonaccian and modular Jaco-type graphs, expanding understanding of their structural characteristics within directed graph theory.

Contribution

It determines the vertex in-degrees for Fibonaccian and modular Jaco-type graphs, addressing a key challenge in understanding their degree distributions.

Findings

Vertex in-degrees for Fibonaccian Jaco-type graphs are characterized.

Vertex in-degrees for modular Jaco-type graphs are characterized.

Provides new insights into the structure of Jaco-type graphs.

Abstract

The concepts of linear Jaco graphs and Jaco-type graphs have been introduced as certain types of directed graphs with specifically defined adjacency conditions. The distinct difference between a pure Jaco graph and a Jaco-type graph is that for a pure Jaco graph, the total vertex degree $d(v)$ is well-defined, while for a Jaco-type graph the vertex out-degree $d^+(v)$ is well-defined. Hence, in the case of pure Jaco graphs a challenge is to determine $d^-(v)$ and $d^+(v)$ respectively and for Jaco-type graphs a challenge is to determine $d^-(v)$. In this paper, the vertex in-degrees for Fibonaccian and modular Jaco-type graphs are determined.