Signed Domination of Oriented Matroid Systems
نویسنده
چکیده
The domination function has played an important part in reliability theory. While most of the work in this field has been restricted to various types of network system models, many of the results can be generalized to much wider families of systems associated with matroids. Previous papers have explored the relation between undirected network systems and matroids. In this paper the main focus is on directed network systems and oriented matroids. Classical results for directed network systems include the fact that the signed domination is either +1 or −1 if the network is acyclic, and zero otherwise. It turns out that these results can be generalized to systems derived from oriented matroids. Several classes of such systems will be discussed.
منابع مشابه
Oriented matroid systems
The domination invariant has played an important part in reliability theory. While most of the work in this field has been restricted to various types of network system models, many of the results can be generalized to much wider families of systems associated with matroids. A matroid is an ordered pair (F,M), where F is a nonempty finite set and M is a collection of incomparable subsets of F ,...
متن کاملSIGNED ROMAN DOMINATION NUMBER AND JOIN OF GRAPHS
In this paper we study the signed Roman dominationnumber of the join of graphs. Specially, we determine it for thejoin of cycles, wheels, fans and friendship graphs.
متن کاملA ug 2 00 5 Las Vergnas cube conjecture and reconstruction properties of the cube matroid February 2 , 2008 Ilda
Las Vergnas Cube Conjecture states that the cube matroid has exactly one class of orientations. We prove that this conjecture is equivalent to saying that the oriented matroid Aff(C), of the affine dependencies of the n-cube C := {−1, 1} over IR, can be reconstructed from the underlying matroid and one of the following partial lists of signed circuits or cocircuits: 1) the signed circuits of ra...
متن کاملFlows in Oriented Matroids
Recently Hochstättler and Nešetřil [3] introduced the flow lattice of an oriented matroid as generalization of the lattice of all integer flows of a digraph or more general a regular matroid. This lattice is defined as the integer hull of the characteristic vectors of signed circuits. We describe the structure and the dimension of the flow lattice for uniform and rank 3 oriented matroids and co...
متن کاملWeak signed Roman domination in graphs
A {em weak signed Roman dominating function} (WSRDF) of a graph $G$ with vertex set $V(G)$ is defined as afunction $f:V(G)rightarrow{-1,1,2}$ having the property that $sum_{xin N[v]}f(x)ge 1$ for each $vin V(G)$, where $N[v]$ is theclosed neighborhood of $v$. The weight of a WSRDF is the sum of its function values over all vertices.The weak signed Roman domination number of $G...
متن کامل