the crossing number of a graph  is the minimum number of edge crossings over all possible drawings of  in a plane. the crossing number is an important measure of the non-planarity of a graph, with applications in discrete and computational geometry and vlsi circuit design. in this paper we introduce vertex centered crossing number and study the same for maximal planar graph.

We show that if a graph G with n ≥ 3 vertices can be drawn in the plane such that each of its edges is involved in at most four crossings, then G has at most 6n− 12 edges. This settles a conjecture of Pach, Radoičić, Tardos, and Tóth. As a corollary we also obtain a better bound for the Crossing Lemma which gives a lower bound for the minimum number of crossings in a drawing of a graph.

Background Given that school-age students, as active road users, are more vulnerable to injury compared with other pedestrians, a large number of them, following an injury, may either fail to go to school at least for a short time or even suffer from disabilities for the rest of their lives. The aim of this study was to determine safe behavior in road crossing using the theory of planned behavi...

In this paper, we discuss a direct measure for aperiodic energy and periodic energy in speech signals. Most measures for aperiodicity have been indirect, such as zero crossing rate, highfrequency energy and the ratio of high-frequency energy to lowfrequency energy. Such indirect measurements will usually fail in situations where there is both strong periodic and aperiodic energy in the speech s...

The expected value for the weighted crossing number of a randomly weighted graph is studied. A variation of the Crossing Lemma for expectations is proved. We focus on the case where the edge-weights are independent random variables that are uniformly distributed on [0, 1].