Counterexamples to an edge spread question for zero forcing number
نویسندگان
چکیده
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 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.
متن کاملThe Forcing Edge-to-vertex Detour Number of a Graph
For two vertices u and v in a graph G = (V, E), the detour distance D (u, v) is the length of a longest u – v path in G. A u – v path of length D (u, v) is called a u – v detour. For subsets A and B of V, the detour distance D (A, B) is defined as D (A, B) = min {D (x, y) : x ∈ A, y ∈ B}. A u – v path of length D (A, B) is called an A – B detour joining the sets A, B V where u ∈ A and v ∈ B. A...
متن کاملMinimum rank and zero forcing number for butterfly networks
The minimum rank of a simple graph G is the smallest possible rank over all symmetric real matrices A whose nonzero off-diagonal entries correspond to the edges of G. Using the zero forcing number, we prove that the minimum rank of the r-th butterfly network is 1 9 [ (3r + 1)2r+1 − 2(−1)r ] and that this is equal to the rank of its adjacency matrix.
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
ژورنال
عنوان ژورنال: Linear Algebra and its Applications
سال: 2014
ISSN: 0024-3795
DOI: 10.1016/j.laa.2014.01.009