Counting-up Method of Topological Finishing Composite Patterns

Part 1 Method of Counting-up cubic Graph by Plane-joint System

Abstract

A topological finishing composite pattern is corresponded 1 by 1 to rooted meta-graph composition as a dual structure. Graph composition which is basic structure of meta-graph composition can be shown as composite pattern of basic line graph, basic plane graph, and basic cubic graph, with dot joint, line joint, plane joint. This study reports an algorithm for counting-up all the pattern of cubic graph, which is important and most complicated graph composition, adopting plane joint system of basic cubic graphs, and shows all the counting-up cubic graph figures from 4 dots to 7dots.