Counting largest mutual-visibility and general position sets of glued $t$-ary trees

TL;DR

This paper determines the extremal sets for mutual-visibility and general position problems in glued t-ary trees, extending previous results from binary trees to more general structures, and provides exact counts for these sets.

Contribution

It extends the analysis of mutual-visibility and general position invariants from binary trees to glued t-ary trees, including exact counts of extremal sets.

Findings

Exact values of invariants for glued binary trees

Extension of results to glued t-ary trees

Enumeration of extremal sets in various configurations

Abstract

All four invariants of the mutual-visibility problem and, all four invariants of the general position problem are determined for glued binary trees. The number of the corresponding extremal sets is obtained in each of the eight situations. The results are further extended to glued $t$-ary trees, and some of them also to generalized glued binary trees.