English (United Kingdom)

https://curated-unify.zendy.io/wp-json/zendy-region/v1/featured_content/oa?rat=en

https://curated-unify.zendy.io/wp-json/zendy-region/v1/highlighted_journal/

Global: Zendy Plus annual

Presents the access of premium content as premium feature

Premium Content

Presents the keyphrase highlighting as premium feature

Keyphrase Highlighting

Presents the summarisation as premium feature

Summarisation

Insights

Presents the pdf analysis as premium feature

PDF Analysis

Presents the zaia usage as premium feature

ZAIA

Global: Zendy Plus monthly

Global: Zendy Tools annual

Global: Zendy Tools monthly

Global: Zendy Free Plan

Zero forcing is a combinatorial game played on a graph with the ultimate goalof changing the colour of all the vertices at minimal cost. Originally thisgame was conceived as a one player game, but later a two-player version wasdevised in-conjunction with studies on the inertia of a graph, and has becomeknown as the $q$-analogue of zero forcing. In this paper, we study and computethe $q$-analogue zero forcing number for various families of graphs. We beginwith by considering a concept of contraction associated with trees. We thensignificantly generalize an equation between this $q$-analogue of zero forcingand a corresponding nullity parameter for all threshold graphs. We close bystudying the $q$-analogue of zero forcing for certain Kneser graphs, and avariety of cartesian products of structured graphs.

The $q$-Analogue of Zero Forcing for Certain Families of Graphs