Domination structure in 3-connected graphs

TL;DR

This paper investigates the structure of 3-connected graphs, focusing on their minimum dominating sets, providing bounds, and presenting a polynomial-time method for their determination.

Contribution

It introduces a new structural analysis of 3-connected graphs and offers a polynomial-time algorithm for finding their minimum dominating sets.

Findings

Upper bounds on the number of structures identified

Minimum dominating set determined in polynomial time

Structural properties of 3-connected graphs elucidated

Abstract

From a recent perspective, the structure of a 3-connected graph is studied in this paper. It stipulates the minimum dominating set of a 3-connected graph. Also, we count the number of structures, as a consequence, the upper bound is obtained. By it, the minimum dominating set of a 3-connected graph is determined in polynomial time.