Irredundance, secure domination and maximum degree in trees
نویسندگان
چکیده
منابع مشابه
Irredundance, secure domination and maximum degree in trees
It is shown that the lower irredundance number and secure domination number of an n vertex tree T with maximum degree 3, are bounded below by 2(n+ 1)/(2 + 3) (T = K1, ) and ( n+ − 1)/(3 − 1), respectively. The bounds are sharp and extremal trees are exhibited. © 2006 Elsevier B.V. All rights reserved. MSC: 05C69
متن کاملDomination and irredundance in tournaments
A set S ⊆ V of vertices in a graph G = (V,E) is called a dominating set if every vertex in V − S is adjacent to at least one vertex in S. Domination in graphs is a well-studied branch of graph theory, and is the subject of two books by Haynes, Hedetniemi and Slater [8, 9]. However, about 90% of the papers on domination have considered only undirected graphs. Thus, relatively little is known abo...
متن کاملDistance Domination and Distance Irredundance in Graphs
A set D ⊆ V of vertices is said to be a (connected) distance k-dominating set of G if the distance between each vertex u ∈ V − D and D is at most k (and D induces a connected graph in G). The minimum cardinality of a (connected) distance k-dominating set in G is the (connected) distance k-domination number of G, denoted by γk(G) (γ c k (G), respectively). The set D is defined to be a total k-do...
متن کاملIsolate Domination Number and Maximum Degree
A subset D of the vertex set V (G) of a graph G is called a dominating set of G if every vertex in V − D is adjacent to a vertex in D. The minimum cardinality of a dominating set is called the domination number and is denoted by γ(G). A dominating set D such that δ(< D >) = 0 is called an isolate dominating set. The minimum cardinality of an isolate dominating set is called the isolate dominati...
متن کاملIrredundance and domination in kings graphs
Each king on an n×n chessboard is said to attack its own square and its neighboring squares, i.e., the nine or fewer squares within one move of the king. A set of kings is said to form an irredundant set if each attacks a square attacked by no other king in the set. We prove that the maximum size of an irredundant set of kings is bounded between (n− 1)=3 and n=3, and that the minimum size of a ...
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: Discrete Mathematics
سال: 2007
ISSN: 0012-365X
DOI: 10.1016/j.disc.2006.05.037