Cyclic Base Ordering of Graphs

TL;DR

This paper investigates cyclic base orderings in various graph families, providing theoretical insights and a polynomial-time algorithm to verify such orderings, enhancing understanding of graph structures and their spanning properties.

Contribution

It introduces new results on cyclic base orderings for multiple graph families and presents an efficient algorithm for verification.

Findings

Cyclic base orderings exist for several graph families.

A polynomial-time algorithm can verify cyclic base orderings.

New theoretical results on graph structures and spanning trees.

Abstract

A cyclic base ordering of a connected graph $G$, is a cyclic ordering of $E(G)$ such that every cyclically consecutive $|V(G)|-1$ edges form a spanning tree. In this project, we study cyclic base ordering of various families of graphs, including square of cycles, wheel graphs, generalized wheel graphs and broken wheel graphs, fan and broken fan graphs, prism graphs, and maximal 2-degenerate graphs. We also provide a polynomial time algorithm to verify any giving edge ordering is a cyclic base ordering.