A Project on Cyclic Ordering of Some Families of Graphs

TL;DR

This paper investigates cyclic base orderings in various classes of graphs, aiming to understand how edges can be cyclically arranged so that consecutive edges form spanning trees.

Contribution

It introduces new results on cyclic base orderings for triangular grid graphs, series compositions, generalized theta graphs, and circulant graphs.

Findings

Established cyclic base orderings for triangular grid graphs

Analyzed cyclic orderings in series compositions of graphs

Extended cyclic ordering concepts to generalized theta and circulant graphs

Abstract

Let $G$ be an $n$-vertex connected graph. A cyclic base ordering of $G$ is a cyclic ordering of all edges such that every cyclically consecutive $n-1$ edges induce a spanning tree of $G$. In this project, we study cyclic base ordering of triangular grid graphs, series composition of graphs, generalized theta graphs, and circulant graphs.