Patriarchy Family Tree Graph from Tiv to Kumator (Seember)

Abstract

Tree graphs, as acyclic and connected structures, provide a framework for modelling hierarchical relationships, such as genealogical lineages. This study constructs and analyzes a patriarchal family tree of the Tiv ethnic group, tracing lineage from Tiv to Kumator, through the application of the Dsatur graph coloring algorithm. Each vertex represents an individual, while edges denote parent–child relationships, forming an acyclic connected graph. By implementing Dsatur, optimal vertex coloring was achieved such that no two adjacent vertices share the same color, confirming the tree’s bipartite nature. The resulting family tree revealed a chromatic number of two, consistent with theoretical predictions for acyclic graphs, and a longest lineage path of fifteen generations. Aside from establishing structural relationships, the model determines how patriarchal lineage rules influence genealogical continuity, illustrating where dynastic extensions cease due to the absence of male descendants.