scholarly journals All Graphs with a Failed Zero Forcing Number of Two

Symmetry ◽  
2021 ◽  
Vol 13 (11) ◽  
pp. 2221
Author(s):  
Luis Gomez ◽  
Karla Rubi ◽  
Jorden Terrazas ◽  
Darren A. Narayan
Keyword(s):  
Zero Forcing ◽  
The Past ◽  
Zero Forcing Number ◽  
Forcing Number ◽  
Repeated Applications ◽  
Zero Forcing Numbers

Given a graph G, the zero forcing number of G, Z(G), is the smallest cardinality of any set S of vertices on which repeated applications of the forcing rule results in all vertices being in S. The forcing rule is: if a vertex v is in S, and exactly one neighbor u of v is not in S, then u is added to S in the next iteration. Zero forcing numbers have attracted great interest over the past 15 years and have been well studied. In this paper, we investigate the largest size of a set S that does not force all of the vertices in a graph to be in S. This quantity is known as the failed zero forcing number of a graph and will be denoted by F(G). We present new results involving this parameter. In particular, we completely characterize all graphs G where F(G)=2, solving a problem posed in 2015 by Fetcie, Jacob, and Saavedra.

Zero forcing number of fuzzy graphs with application

2020 ◽  
Vol 39 (3) ◽  
pp. 3873-3882
Author(s):  
Asefeh Karbasioun ◽  
R. Ameri
Keyword(s):  
Upper Bounds ◽  
Zero Forcing ◽  
Medical Treatments ◽  
Zero Forcing Number ◽  
Fuzzy Graphs ◽  
Forcing Number ◽  
Zero Forcing Numbers ◽  
Forcing Set ◽  
Zero Forcing Set

We introduce and study forcing number for fuzzy graphs. Also, we compute zero forcing numbers for some classes of graphs and extend this concept to fuzzy graphs. In this regard we obtain upper bounds for zero forcing of some classes of fuzzy graphs. We will proceed to obtain a new algorithm to computing zero forcing set and finding a formula for zero forcing number, and by some examples we illustrate these notions. Finally, we introduce some applications of fuzzy zero forcing in medical treatments.

Zero forcing number of a graph in terms of the number of pendant vertices

2018 ◽  
Vol 68 (7) ◽  
pp. 1424-1433 ◽  
Author(s):  
Xinlei Wang ◽  
Dein Wong ◽  
Yuanshuai Zhang
Keyword(s):  
Zero Forcing ◽  
Zero Forcing Number ◽  
Forcing Number

scholarly journals Path cover number, maximum nullity, and zero forcing number of oriented graphs and other simple digraphs

2015 ◽  
Vol 8 (1) ◽  
pp. 147-167 ◽  
Author(s):  
Adam Berliner ◽  
Cora Brown ◽  
Joshua Carlson ◽  
Nathanael Cox ◽  
Leslie Hogben ◽  
...  
Keyword(s):  
Zero Forcing ◽  
Oriented Graphs ◽  
Path Cover ◽  
Zero Forcing Number ◽  
Maximum Nullity ◽  
Forcing Number ◽  
Path Cover Number

scholarly journals A lower bound on the zero forcing number

2018 ◽  
Vol 250 ◽  
pp. 363-367 ◽  
Author(s):  
Randy Davila ◽  
Thomas Kalinowski ◽  
Sudeep Stephen
Keyword(s):  
Lower Bound ◽  
Zero Forcing ◽  
Zero Forcing Number ◽  
Forcing Number

scholarly journals The Bipartite Zero Forcing Set for a Full Sign Pattern Matrix

Mathematics ◽  
2020 ◽  
Vol 8 (3) ◽  
pp. 354
Author(s):  
Gu-Fang Mou ◽  
Tian-Fei Wang ◽  
Zhong-Shan Li
Keyword(s):  
Sign Pattern ◽  
Zero Forcing ◽  
Minimum Rank ◽  
Zero Forcing Number ◽  
Maximum Nullity ◽  
New Variant ◽  
Forcing Number ◽  
Pattern Matrix ◽  
Forcing Set ◽  
Zero Forcing Set

For an m × n sign pattern P, we define a signed bipartite graph B ( U , V ) with one set of vertices U = { 1 , 2 , … , m } based on rows of P and the other set of vertices V = { 1 ′ , 2 ′ , … , n ′ } based on columns of P. The zero forcing number is an important graph parameter that has been used to study the minimum rank problem of a matrix. In this paper, we introduce a new variant of zero forcing set−bipartite zero forcing set and provide an algorithm for computing the bipartite zero forcing number. The bipartite zero forcing number provides an upper bound for the maximum nullity of a square full sign pattern P. One advantage of the bipartite zero forcing is that it can be applied to study the minimum rank problem for a non-square full sign pattern.

scholarly journals Critical ideals, minimum rank and zero forcing number

2019 ◽  
Vol 358 ◽  
pp. 305-313 ◽  
Author(s):  
Carlos A. Alfaro ◽  
Jephian C.-H. Lin
Keyword(s):  
Zero Forcing ◽  
Minimum Rank ◽  
Zero Forcing Number ◽  
Forcing Number

Maximum nullity and zero forcing number on graphs with maximum degree at most three

2020 ◽  
Vol 284 ◽  
pp. 179-194
Author(s):  
Meysam Alishahi ◽  
Elahe Rezaei-Sani ◽  
Elahe Sharifi
Keyword(s):  
Maximum Degree ◽  
Zero Forcing ◽  
Zero Forcing Number ◽  
Maximum Nullity ◽  
Forcing Number

scholarly journals Some bounds on the zero forcing number of a graph

2018 ◽  
Vol 236 ◽  
pp. 203-213 ◽  
Author(s):  
Michael Gentner ◽  
Dieter Rautenbach
Keyword(s):  
Zero Forcing ◽  
Zero Forcing Number ◽  
Forcing Number
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