We study the strong gravitational lensing properties of galaxy clusters obtained from N-body simulations with standard ΛCDM cosmology. We have used the 32 most massive clusters from a simulation at various redshifts and ray-traced through the clusters to investigate the giant arcs statistics. We have found that ∼ 40 − 50% of the clusters that produce giant arcs give multiple arcs, which agrees ...

Abstract. In this paper, connected domination in fuzzy graphs using strong arcs is introduced. The strong connected domination number of different classes of fuzzy graphs is obtained. An upper bound for the strong connected domination number of fuzzy graphs is obtained. Strong connected domination in fuzzy trees is studied. It is established that the set of fuzzy cut nodes of a fuzzy tree is a ...

In this paper we introduce the concept of strong total domination in fuzzy graphs. We determine the strong total domination number for several classes of fuzzy graphs. A lower bound and an upper bound for the strong total domination number in terms of strong domination number is obtained. Strong total domination in fuzzy trees is studied. A necessary and sufficient condition for the set of fuzz...

We study the strong gravitational lensing properties of galaxy clusters obtained from N-body simulations with standard ΛCDM cosmology. We have used the 32 most massive clusters from a simulation at various redshifts and ray-traced through the clusters to investigate the giant arcs statistics. We have found that ∼ 40 − 50% of the clusters that produce giant arcs give multiple arcs, which agrees ...

A multipartite tournament is an orientation of a complete c-partite graph. In [L. Volkmann, A remark on cycles through an arc in strongly connected multipartite tournaments, Appl. Math. Lett. 20 (2007) 1148–1150], Volkmann proved that a strongly connected cpartite tournament with c > 3 contains an arc that belongs to a directed cycle of length m for every m ∈ {3, 4, . . . , c}. He also conjectu...

A tournament is a digraph, where there is precisely one arc between every pair of distinct vertices. An arc is pancyclic in a digraph D, if it belongs to a cycle of length l, for all 3 <= l <= |V (D)|. Let p(D) denote the number of pancyclic arcs in a digraph D and let h(D) denote the maximum number of pancyclic arcs belonging to the same Hamilton cycle of D. Note that p(D) >= h(D). Moon showed...

Mechano-transduction is an emerging but still poorly understood component of T cell activation. Here we investigated the ligand-dependent contribution made by contractile actomyosin arcs populating the peripheral supramolecular activation cluster (pSMAC) region of the immunological synapse (IS) to T cell receptor (TCR) microcluster transport and proximal signaling in primary mouse T cells. Usin...

Answering a question of Adrian Bondy [4], we prove that every strong digraph has a spanning strong subgraph with at most n + 2α − 2 arcs, where α is the size of a maximum stable set of D. Such a spanning subgraph can be found in polynomial time. An infinite family of oriented graphs for which this bound is sharp was given by Odile Favaron [3]. A direct corollary of our result is that there exis...