A tight upper bound for 2-rainbow domination in generalized Petersen graphs
نویسندگان
چکیده
منابع مشابه
A tight upper bound for 2-rainbow domination in generalized Petersen graphs
Let f be a function that assigns to each vertex a subset of colors chosen from a set C = {1, 2, . . . , k} of k colors. If u∈N(v) f (u) = C for each vertex v ∈ V with f (v) = ∅, then f is called a k-rainbow dominating function (kRDF) of G where N(v) = {u ∈ V | uv ∈ E}. The weight of f , denoted by w(f ), is defined as w(f ) = v∈V |f (v)|. Given a graph G, the minimum weight among all weight...
متن کامل2-rainbow domination in generalized Petersen graphs P(n, 3)
Assume we have a set of k colors and we assign an arbitrary subset of these colors to each vertex of a graph G. If we require that each vertex to which an empty set is assigned has in its neighborhood all k colors, then this assignment is called a k-rainbow dominating function of G. The corresponding invariant γrk(G), which is the minimum sum of numbers of assigned colors over all vertices of G...
متن کاملThe 2-rainbow bondage number in generalized Petersen graphs
Abstract: A 2-rainbow domination function of a graph G = (V, E) is a function f mapping each vertex v to a subset of {1, 2} such that ⋃ u∈N(v) f (u) = {1, 2} when f (v) = �, where N(v) is the open neighborhood of v. The weight of f is denoted by wf (G) = ∑ v∈V �f (v)�. The 2-rainbow domination number, denoted by r2(G), is the smallest wf (G) among all 2-rainbow domination functions f of G. The ...
متن کاملRoman domination number of Generalized Petersen Graphs P(n, 2)
A Roman domination function on a graph G = (V,E) is a function f : V (G) → {0, 1, 2} satisfying the condition that every vertex u with f(u) = 0 is adjacent to at least one vertex v with f(v) = 2. The weight of a Roman domination function f is the value f(V (G)) = ∑ u∈V (G) f(u). The minimum weight of a Roman dominating function on a graph G is called the Roman domination number of G, denoted by...
متن کاملOn Power Domination of Generalized Petersen Graphs
The power dominating problem is a variation of the classical domination problem in graphs. Electricity company use phase measurement units (PMUs) to produce the measuring data of a system, and use these data to estimate states of the system. Because of the high cost of PMUs, minimizing the number of PMUs on a system is an important problem for electricity companies. This problem can be modeled ...
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 Applied Mathematics
سال: 2013
ISSN: 0166-218X
DOI: 10.1016/j.dam.2013.02.031