نتایج جستجو برای: signed total roman k domination

تعداد نتایج: 1181862  

2016
Jernej Azarija Yoomi Rho Seungbo Sim

The Fibonacci cube Γn is the subgraph of the n-dimensional cube Qn induced by the vertices that contain no two consecutive 1s. Using integer linear programming, exact values are obtained for γt(Γn), n ≤ 12. Consequently, γt(Γn) ≤ 2Fn−10 + 21Fn−8 holds for n ≥ 11, where Fn are the Fibonacci numbers. It is proved that if n ≥ 9, then γt(Γn) ≥ d(Fn+2 − 11)/(n− 3)e−1. Using integer linear programmin...

Journal: :Mathematics 2021

For a simple graph G=(V,E) with no isolated vertices, total Roman {3}-dominating function(TR3DF) on G is function f:V(G)→{0,1,2,3} having the property that (i) ∑w∈N(v)f(w)≥3 if f(v)=0; (ii) ∑w∈N(v)f(w)≥2 f(v)=1; and (iii) every vertex v f(v)≠0 has neighbor u f(u)≠0 for v∈V(G). The weight of TR3DF f sum f(V)=∑v∈V(G)f(v) minimum called {3}-domination number denoted by γt{R3}(G). In this paper, we...

2007
Ermelinda DeLaViña Douglas B. West

We limit our discussion to graphs that are simple and finite of order . Although 8 we often identify a graph with its set of vertices, in cases where we need to be K explicit we write . A set of vertices of is said to Z ÐKÑ Q K dominate K provided each vertex of is either in or adjacent to a vertex of . K Q Q The domination number of is the minimum order of a dominating set. A K dominating prov...

2012
S. A. Mane B. N. Waphare

In this paper we consider the (d, n)-domination number, γd,n(Qn), the distance-d domination number γd(Qn) and the connected distance-d domination number γc,d(Qn) of ndimensional hypercube graphs Qn. We show that for 2 ≤ d ≤ bn/2c, and n ≥ 4, γd,n(Qn) ≤ 2n−2d+2, improving the bound of Xie and Xu [19]. We also show that γd(Qn) ≤ 2n−2d+2−r, for 2 − 1 ≤ n − 2d + 1 < 2 − 1, and γc,d(Qn) ≤ 2n−d, for ...

Journal: :Discussiones Mathematicae Graph Theory 2015
Abdollah Khodkar Babak Samadi Lutz Volkmann

Let G be a graph. A function f : V (G) → {−1, 1} is a signed kindependence function if the sum of its function values over any closed neighborhood is at most k − 1, where k ≥ 2. The signed k-independence number of G is the maximum weight of a signed k-independence function of G. Similarly, the signed total k-independence number of G is the maximum weight of a signed total k-independence functio...

Journal: :Czechoslovak Mathematical Journal 2006

Journal: :Discrete Applied Mathematics 2014
Toshimasa Ishii Hirotaka Ono Yushi Uno

Given a graph G = (V, E) of order n and an n-dimensional non-negative vector d = (d(1), d(2), . . . , d(n)), called demand vector, the vector domination (resp., total vector domination) is the problem of finding a minimum S ⊆ V such that every vertex v in V \S (resp., in V ) has at least d(v) neighbors in S. The (total) vector domination is a generalization of many dominating set type problems,...

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