Displaying similar documents to “On 𝖿 -wise arc forwarding index and wavelength allocations in faulty all-optical hypercubes”

Acyclic orientations with path constraints

Rosa M. V. Figueiredo, Valmir C. Barbosa, Nelson Maculan, Cid C. de Souza (2008)

RAIRO - Operations Research - Recherche Opérationnelle

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Many well-known combinatorial optimization problems can be stated over the set of acyclic orientations of an undirected graph. For example, acyclic orientations with certain diameter constraints are closely related to the optimal solutions of the vertex coloring and frequency assignment problems. In this paper we introduce a linear programming formulation of acyclic orientations with path constraints, and discuss its use in the solution of the vertex coloring problem and some versions...

Kernels in the closure of coloured digraphs

Hortensia Galeana-Sánchez, José de Jesús García-Ruvalcaba (2000)

Discussiones Mathematicae Graph Theory

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Let D be a digraph with V(D) and A(D) the sets of vertices and arcs of D, respectively. A kernel of D is a set I ⊂ V(D) such that no arc of D joins two vertices of I and for each x ∈ V(D)∖I there is a vertex y ∈ I such that (x,y) ∈ A(D). A digraph is kernel-perfect if every non-empty induced subdigraph of D has a kernel. If D is edge coloured, we define the closure ξ(D) of D the multidigraph with V(ξ(D)) = V(D) and A ( ξ ( D ) ) = ⋃ i ( u , v ) w i t h c o l o u r i t h e r e e x i s t s a m o n o c h r o m a t i c p a t h o f c o l o u r i f r o m t h e v e r t e x u t o t h e v e r t e x v c o n t a i n e d i n D . Let T₃ and C₃ denote the transitive tournament of order 3 and the 3-cycle,...

On the heights of power digraphs modulo n

Uzma Ahmad, Husnine Syed (2012)

Czechoslovak Mathematical Journal

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A power digraph, denoted by G ( n , k ) , is a directed graph with ℤ n = { 0 , 1 , ⋯ , n - 1 } as the set of vertices and E = { ( a , b ) : a k ≡ b ( mod n ) } as the edge set. In this paper we extend the work done by Lawrence Somer and Michal Křížek: On a connection of number theory with graph theory, Czech. Math. J. 54 (2004), 465–485, and Lawrence Somer and Michal Křížek: Structure of digraphs associated with quadratic congruences with composite moduli, Discrete Math. 306 (2006), 2174–2185. The heights of the vertices and the components of G ( n , k ) for n ≥ 1 and...