On the Semitotal Forcing Number of a Graph

2022 ◽  
Author(s):  
Qin Chen
Keyword(s):  
Forcing Number

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.

On Tight Bounds for the k-Forcing Number of a Graph

2017 ◽  
Vol 42 (2) ◽  
pp. 743-749
Author(s):  
Yan Zhao ◽  
Lily Chen ◽  
Hengzhe Li
Keyword(s):  
Forcing Number

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 The forcing number of graphs with given girth

2017 ◽  
Vol 41 (2) ◽  
pp. 189-204 ◽  
Author(s):  
Randy Davila ◽  
Michael A. Henning
Keyword(s):  
Forcing Number

scholarly journals On the total forcing number of a graph

2019 ◽  
Vol 257 ◽  
pp. 115-127 ◽  
Author(s):  
Randy Davila ◽  
Michael A. Henning
Keyword(s):  
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.

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