Half domination arrangements in regular and semi-regular tessellation type graphs

TL;DR

This paper investigates half-domination sets in infinite vertex transitive graphs derived from regular and semi-regular tessellations, providing sharp results and bounds on vertex densities.

Contribution

It introduces new bounds and sharp results for half-domination sets in tessellation-based graphs, expanding understanding of their structural properties.

Findings

Sharp results for some tessellation graphs

Upper bounds on average densities of half-domination sets

Extension of domination concepts to infinite tessellation graphs

Abstract

We study the problem of half-domination sets of vertices in vertex transitive infinite graphs generated by regular or semi-regular tessellations of the plane. In some cases, the results obtained are sharp and in the rest, we show upper bounds for the average densities of vertices in half-domination sets.