Powered by OpenAIRE graph
Found an issue? Give us feedback
image/svg+xml art designer at PLoS, modified by Wikipedia users Nina, Beao, JakobVoss, and AnonMoos Open Access logo, converted into svg, designed by PLoS. This version with transparent background. http://commons.wikimedia.org/wiki/File:Open_Access_logo_PLoS_white.svg art designer at PLoS, modified by Wikipedia users Nina, Beao, JakobVoss, and AnonMoos http://www.plos.org/ AppliedMatharrow_drop_down
image/svg+xml art designer at PLoS, modified by Wikipedia users Nina, Beao, JakobVoss, and AnonMoos Open Access logo, converted into svg, designed by PLoS. This version with transparent background. http://commons.wikimedia.org/wiki/File:Open_Access_logo_PLoS_white.svg art designer at PLoS, modified by Wikipedia users Nina, Beao, JakobVoss, and AnonMoos http://www.plos.org/
AppliedMath
Article . 2025 . Peer-reviewed
License: CC BY
image/svg+xml art designer at PLoS, modified by Wikipedia users Nina, Beao, JakobVoss, and AnonMoos Open Access logo, converted into svg, designed by PLoS. This version with transparent background. http://commons.wikimedia.org/wiki/File:Open_Access_logo_PLoS_white.svg art designer at PLoS, modified by Wikipedia users Nina, Beao, JakobVoss, and AnonMoos http://www.plos.org/
AppliedMath
Article . 2025 . Peer-reviewed
License: CC BY
Data sources: Crossref
image/svg+xml art designer at PLoS, modified by Wikipedia users Nina, Beao, JakobVoss, and AnonMoos Open Access logo, converted into svg, designed by PLoS. This version with transparent background. http://commons.wikimedia.org/wiki/File:Open_Access_logo_PLoS_white.svg art designer at PLoS, modified by Wikipedia users Nina, Beao, JakobVoss, and AnonMoos http://www.plos.org/
AppliedMath
Article . 2025
Data sources: DOAJ
versions View all 3 versions
addClaim

Failed Skew Zero Forcing Numbers of Path Powers and Circulant Graphs

Authors: Aidan Johnson; Andrew Vick; Rigoberto Flórez; Darren A. Narayan;

Failed Skew Zero Forcing Numbers of Path Powers and Circulant Graphs

Abstract

For a graph G, the zero forcing number of G, Z(G), is defined to be the minimum cardinality of a set S of vertices for which repeated applications of the forcing rule results in all vertices being in S. The forcing rule is as follows: if a vertex v is in S, and exactly one neighbor u of v is not in S, then the vertex u is added to S in the subsequent iteration. Now, the failed zero forcing number of a graph is defined to be the maximum size of a set of vertices which does not force all of the vertices in the graph. A similar type of forcing is called skew zero forcing, which is defined so that if there is exactly one neighbor u of v that is not in S, then the vertex u is added to S in the next iteration. The key difference is that vertices that are not in S can force other vertices. The failed skew zero forcing number of a graph is denoted by F−(G). At its core, the problem we consider is how to identify the tipping point at which information or infection will spread through a network or a population. The graphs we consider are where computers/routers or people are arranged in a linear or circular formation with varying proximities for contagion. Here, we present new results for failed skew zero forcing numbers of path powers and circulant graphs. Furthermore, we found that the failed skew zero forcing numbers of these families form interesting sequences with increasing n.

Related Organizations
Keywords

QA1-939, failed zero forcing, path powers, circulant graphs, Mathematics, zero forcing

  • BIP!
    Impact byBIP!
    selected citations
    These citations are derived from selected sources.
    This is an alternative to the "Influence" indicator, which also reflects the overall/total impact of an article in the research community at large, based on the underlying citation network (diachronically).
    0
    popularity
    This indicator reflects the "current" impact/attention (the "hype") of an article in the research community at large, based on the underlying citation network.
    Average
    influence
    This indicator reflects the overall/total impact of an article in the research community at large, based on the underlying citation network (diachronically).
    Average
    impulse
    This indicator reflects the initial momentum of an article directly after its publication, based on the underlying citation network.
    Average
Powered by OpenAIRE graph
Found an issue? Give us feedback
selected citations
These citations are derived from selected sources.
This is an alternative to the "Influence" indicator, which also reflects the overall/total impact of an article in the research community at large, based on the underlying citation network (diachronically).
BIP!Citations provided by BIP!
popularity
This indicator reflects the "current" impact/attention (the "hype") of an article in the research community at large, based on the underlying citation network.
BIP!Popularity provided by BIP!
influence
This indicator reflects the overall/total impact of an article in the research community at large, based on the underlying citation network (diachronically).
BIP!Influence provided by BIP!
impulse
This indicator reflects the initial momentum of an article directly after its publication, based on the underlying citation network.
BIP!Impulse provided by BIP!
0
Average
Average
Average
gold