4 We prove that a number of natural problems concerning the existence of arc-disjoint directed 5 and “undirected” (spanning) subdigraphs in a digraph are NP-complete. Among these are the 6 following of which the first settles an open problem due to Thomassé (see e.g. [1, Problem 9.9.7] 7 and [3, 5]) and the second settles an open problem posed in [3]. 8 • Given a directed graph D and a vertex s...

In this paper, the concept of a strong n-Connected Total Perfect k-connected total perfect k-dominating set and weak n-connected in fuzzy graphs is introduced. current work, triple-connected dominating modified to an nctpkD(G) number γnctpD(G). New definitions are compared with old ones. Strong obtained. The results those sets discussed spanning graphs, arcs, sets, generalization complete, conn...

MOTIVATION The goal of motif discovery is to detect novel, unknown, and important signals from biology sequences. In most models, the importance of a motif is equal to the sum of the similarity of every single position. In 2006, Song et al. introduced Aggregated Related Column Score (ARCS) measure which includes correlation information to the evaluation of motif importance. The paper showed tha...

A dicycle cover of a digraphD is a familyF of dicycles ofD such that each arc ofD lies in at least one dicycle inF. We investigate the problem of determining the upper bounds for the minimum number of dicycles which cover all arcs in a strong digraph. Best possible upper bounds of dicycle covers are obtained in a number of classes of digraphs including strong tournaments, Hamiltonian oriented g...

In [6], Thomassen conjectured that if I is a set of k − 1 arcs in a k-strong tournament T , then T − I has a Hamiltonian cycle. This conjecture was proved by Fraisse and Thomassen [3]. We prove the following stronger result. Let T = (V, A) be a k-strong tournament on n vertices and let X1, X2, . . . , Xl be a partition of the vertex set V of T such that |X1| ≤ |X2| ≤ . . . ≤ |Xl|. If k ≥ ∑l−1 i...

We present a detailed investigation into which properties of cold dark matter halos make them effective strong gravitational lenses. The cross sections for giant arc formation of 878 clusters from a high-resolution N-body simulation of the ΛCDM cosmology are measured by ray tracing through 13,594 unique projections. We measure concentrations, axis ratios, orientations, and the amount of substru...