The Z_q-forcing number for some graph families

2023/05/19 by Jorge Blanco, Blanco, Jorge, Stephanie Einstein +7 · 1 citation
Computer Science · Decision Sciences · #Advanced Graph Theory Research #Artificial Intelligence in Games #Combinatorics (math.CO) #FOS: Mathematics #Game Theory and Applications

paper · pdf · doi:10.48550/arxiv.2305.11748

openalex publication_date 2023/05/19 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

The zero forcing number was introduced as a combinatorial bound on the maximum nullity taken over the set of real symmetric matrices that respect the pattern of an underlying graph. The Z_q-forcing game is an analog to the standard zero forcing game which incorporates inertia restrictions on the set of matrices associated with a graph. This work proves an upper bound on the Z_q-forcing number for trees. Furthermore, we consider the Z_q-forcing number for caterpillar cycles on n vertices. We focus on developing game theoretic proofs of upper and lower bounds.

Cited by

• On the Z_q-forcing number: computational approach and exact values

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• Proof of a conjecture on the zero forcing number of a graph