The crossing number of a graph G is the minimum number of pairwise intersections of edges among all drawings of G. In this paper, we study the crossing number of Kn,n − nK2, Kn × P2, Kn × P3 and Kn × C4.

where En are measurable sets. Let > 0. Since μ is outer regular, and inner regular on measurable sets of finite measure, there exist an open set On and a compact set Kn such that Kn ⊂ En ⊂ On μ(En)− 1 2N < μ(Kn) ≤ μ(En) ≤ μ(On) < μ(En) + 1 2N thus Kn ⊂ On and μ(On)− μ(Kn) < 1 N , and since X is of finite measure, we have μ(On \Kn) < 1 N consider the closed sets Kn and O c n. By Urysohn’s Lemma,...

The effect of Ca(2+)/calmodulin-dependent protein kinase II (CaMK II) on voltage-gated ion channels is widely studied through the use of specific CaMK II blockers such as 2-[N-(2-hydroxyethyl)]-N-(4methoxybenzenesulfonyl)]amino-N-(4-chlorocinnamyl)-N-methylbenzylamine (KN-93). The present study demonstrates that KN-93 is a direct extracellular blocker of a wide range of cloned Kv channels from ...

Let K n denote the Cartesian product Kn Kn Kn, where Kn is the complete graph on n vertices. We show that the domination number of K n is ⌈

In this paper, we show that of all graphs of order n with matching number β, the graphs with maximal spectral radius are Kn if n = 2β or 2β + 1; K2β+1 ∪Kn−2β−1 if 2β + 2 n < 3β + 2; Kβ ∨ Kn−β or K2β+1 ∪Kn−2β−1 if n = 3β + 2; Kβ ∨ Kn−β if n > 3β + 2, where Kt is the empty graph on t vertices. © 2006 Elsevier Inc. All rights reserved. AMS classification: 05C35; 05C50

Let Kn − e be a graph obtained from a complete graph of order n by dropping an edge, and let G p be a Paley graph of order p. It is shown that if G p contains no Kn−e, then r(Kn+1−e) ≥ 2p+1. For example, G1493 contains no K13 − e, so r(K14 − e) ≥ 2987, improving the old bound 2557. It is also shown that r(K2 + G) ≤ 4r(G, K2 + G)− 2, implying that r(Kn − e) ≤ 4 r(Kn−2, Kn − e)− 2. c © 2007 Elsev...