Construction numbers: How to build a graph?
arXiv:2302.13186v61 citationsh-index: 20
Originality Synthesis-oriented
AI Analysis
This work addresses a combinatorial enumeration problem in graph theory, likely incremental as it extends known results to specific families.
The paper tackled the problem of counting construction sequences for graphs, where edges must follow their endpoints, and determined the construction numbers for various graph families.
A construction sequence for a graph is a listing of the elements of the graph (the set of vertices and edges) such that each edge follows both its endpoints. The construction number of the graph is the number of such sequences. We determine this number for various graph families.