Work

Exploring the influence of graph operations on zero forcing sets

Year: 2025

Type: article

Abstract: Zero forcing in graphs is a coloring process where a vertex colored blue can force its unique uncolored neighbor to be colored blue. A zero forcing set is a set of initially blue vertices capable of eventually coloring all vertices of the graph. In this paper, we focus on the numbers z ( G ; i ) , which is the number of zero forcing sets of size i of the graph G . These numbers were initially studied by Boyer et al. [5] where they conjectured that for any graph G on n vertices, z ( G ; i ) ≤ z ( P n ; i ) for all i ≥ 1 where P n is the path graph on n vertices. The main aim of this paper is to show that several classes of graphs, including outerplanar graphs and threshold graphs, satisfy this conjecture. We do this by studying various graph operations and examining how they affect the number of zero forcing sets.

Source: Discrete Mathematics

DOI: 10.1016/j.disc.2025.114516

Authors: Krishna Menon, Anurag Singh

Institutions: KTH Royal Institute of Technology, Indian Institute of Technology Bhilai

Language: English

Topic: Advanced Graph Theory Research

Subfield: Computational Theory and Mathematics

Field: Computer Science

Domain: Physical Sciences

Open Access status: hybrid

Estimated APC paid: $3,320

Funders: Infosys Foundation, Science and Engineering Research Board