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.

Let $R$ be a commutative ring with identity and $M$ be an unitary $R$-module. The intersection graph of an $R$-module $M$, denoted by $Gamma(M)$, is a simple graph whose vertices are all non-trivial submodules of $M$ and two distinct vertices $N_1$ and $N_2$ are adjacent if and only if $N_1cap N_2neq 0$. In this article, we investigate the concept of a planar intersection graph and maximal subm...

We consider the problem of determining the maximum and the minimum number of upward planar orientations a maximal planar graph can have. We show that n-vertex maximal planar graphs have at least Ω(n · 1.189) and at most O(n · 4) upward planar orientations. Moreover, there exist n-vertex maximal planar graphs having as few as O(n · 2) upward planar orientations and n-vertex maximal planar graphs...