منابع مشابه
On the zero forcing number of some Cayley graphs
Let Γa be a graph whose each vertex is colored either white or black. If u is a black vertex of Γ such that exactly one neighbor v of u is white, then u changes the color of v to black. A zero forcing set for a Γ graph is a subset of vertices Zsubseteq V(Γ) such that if initially the vertices in Z are colored black and the remaining vertices are colored white, then Z changes the col...
متن کاملZero forcing number of graphs
A subset S of initially infected vertices of a graph G is called forcing if we can infect the entire graph by iteratively applying the following process. At each step, any infected vertex which has a unique uninfected neighbour, infects this neighbour. The forcing number of G is the minimum cardinality of a forcing set in G. In the present paper, we study the forcing number of various classes o...
متن کاملZero forcing in iterated line digraphs
Zero forcing is a propagation process on a graph, or digraph, defined in linear algebra to provide a bound for the minimum rank problem. Independently, zero forcing was introduced in physics, computer science and network science, areas where line digraphs are frequently used as models. Zero forcing is also related to power domination, a propagation process that models the monitoring of electric...
متن کاملFractional zero forcing via three-color forcing games
An r-fold analogue of the positive semidefinite zero forcing process that is carried out on the r-blowup of a graph is introduced and used to define the fractional positive semidefinite forcing number. Properties of the graph blowup when colored with a fractional positive semidefinite forcing set are examined and used to define a three-color forcing game that directly computes the fractional po...
متن کاملThe Zero Forcing Number of Circulant Graphs
The zero forcing number of a graph G is the cardinality of the smallest subset of the vertices of G that forces the entire graph using a color change rule. This paper presents some basic properties of circulant graphs and later investigates zero forcing numbers of circulant graphs of the form C[n, {s, t}], while also giving attention to propagation time for specific zero forcing sets.
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ژورنال
عنوان ژورنال: Proyecciones (Antofagasta)
سال: 2019
ISSN: 0717-6279
DOI: 10.22199/issn.0717-6279-2019-05-0064