Maximal Buttonings of Non-Tree Graphs

Wanchai Tapanyo, Pradthana Jaipong

Abstract

Let G be a finite connected graph of n vertices v1, v2, . . . , vn. A
buttoning of G is a closed walk consisting of n shortest paths

[v1, v2], [v2, v3], . . . , [vn−1, vn], [vn, v1].

The buttoning is said to be maximal if it has a maximum length when compared
with all other buttonings of G. The goal of this work is to find a length of a
maximal buttoning of non-tree graphs: complete multipartite graphs, grid graphs
and rooted products of graphs.