3D Visibility Representations of 1-planar Graphs

We prove that every 1-planar graph G has a z-parallel visibility representation, i.e., a 3D visibility representation in which the vertices are isothetic disjoint rectangles parallel to the xy-plane, and the edges are unobstructed z-parallel visibilities between pairs of rectangles. In addition, the constructed representation is such that there is a plane that intersects all the rectangles, and this intersection defines a bar 1-visibility representation of G.Comment: Appears in the Proceedings of the 25th International Symposium on Graph Drawing and Network Visualization (GD 2017

The Antibody Targeting the E314 Peptide of Human Kv1.3 Pore Region Serves as a Novel, Potent and Specific Channel Blocker

Selective blockade of Kv1.3 channels in effector memory T (TEM) cells was validated to ameliorate autoimmune or autoimmune-associated diseases. We generated the antibody directed against one peptide of human Kv1.3 (hKv1.3) extracellular loop as a novel and possible Kv1.3 blocker. One peptide of hKv1.3 extracellular loop E3 containing 14 amino acids (E314) was chosen as an antigenic determinant to generate the E314 antibody. The E314 antibody specifically recognized 63.8KD protein stably expressed in hKv1.3-HEK 293 cell lines, whereas it did not recognize or cross-react to human Kv1.1(hKv1.1), Kv1.2(hKv1.2), Kv1.4(hKv1.4), Kv1.5(hKv1.5), KCa3.1(hKCa3.1), HERG, hKCNQ1/hKCNE1, Nav1.5 and Cav1.2 proteins stably expressed in HEK 293 cell lines or in human atrial or ventricular myocytes by Western blotting analysis and immunostaining detection. By the technique of whole-cell patch clamp, the E314 antibody was shown to have a directly inhibitory effect on hKv1.3 currents expressed in HEK 293 or Jurkat T cells and the inhibition showed a concentration-dependence. However, it exerted no significant difference on hKv1.1, hKv1.2, hKv1.4, hKv1.5, hKCa3.1, HERG, hKCNQ1/hKCNE1, L-type Ca2+ or voltage-gated Na+ currents. The present study demonstrates that the antibody targeting the E314 peptide of hKv1.3 pore region could be a novel, potent and specific hKv1.3 blocker without affecting a variety of closely related Kv1 channels, KCa3.1 channels and functional cardiac ion channels underlying central nervous systerm (CNS) disorders or drug-acquired arrhythmias, which is required as a safe clinic-promising channel blocker

(a,d)-edge-antimagic total labelings of caterpillars

For a graph G = (V,E), a bijection g from V (G)∪E(G) into {1, 2, ..., |V (G)|+|E(G)|} is called (a, d)-edge-antimagic total labeling of G if the edge-weights w(xy) = g(x) + g(y) + g(xy), xy ∈ E(G), form an arithmetic progression with initial term a and common difference d. An (a, d)-edge-antimagic total labeling g is called super (a, d)-edge-antimagic total if g(V (G)) = {1, 2, ..., |V (G)|}. We study super (a, d)-edge-antimagic total properties of stars Sn and caterpillar Sn1,n2,...,nr .C

Vertex-antimagic labelings of regular graphs

Let G = (V,E) be a finite, simple and undirected graph with p vertices and q edges. An (a, d)-vertex-antimagic total labeling of G is a bijection f from V (G) ∪ E(G) onto the set of consecutive integers 1, 2, …, p + q, such that the vertex-weights form an arithmetic progression with the initial term a and difference d, where the vertex-weight of x is the sum of the value f(x) assigned to the vertex x together with all values f(xy) assigned to edges xy incident to x. Such labeling is called super if the smallest possible labels appear on the vertices. In this paper, we study the properties of such labelings and examine their existence for 2r-regular graphs when the difference d is 0, 1, …, r + 1.Web of Science2891874186