Orthogonal drawings and crossing numbers of the Kronecker product of two cycles

Authors:
Pranava K. Jha;Savitri Devisetty
Affiliations:
-;-
Venue:
Journal of Parallel and Distributed Computing
Year:
2012

Citing 19
Cited 0

The Architecture of FAIM-1

Computer
The crossing number of C4 × C4

Journal of Graph Theory
Doing the Twist: Diagonal Meshes Are Isomorphic to Twisted Toroidal Meshes

IEEE Transactions on Computers
Embeddings of star graphs into optical meshes without bends

Journal of Parallel and Distributed Computing
Kronecker products of paths and cycles: decomposition, factorization and bi-pancyclicity

Discrete Mathematics - Special issue on Graph theory
Graph drawing and its applications

Drawing graphs
Graph Drawing: Algorithms for the Visualization of Graphs

Graph Drawing: Algorithms for the Visualization of Graphs
On the Computational Complexity of Upward and Rectilinear Planarity Testing

SIAM Journal on Computing
Improved Approximations of Crossings in Graph Drawings and VLSI Layout Areas

SIAM Journal on Computing
Diagonal and Toroidal Mesh Networks

IEEE Transactions on Computers
Perfect r-domination in the Kronecker product of two cycles, with an application to diagonal/toroidal mesh

Information Processing Letters
Arrangements, circular arrangements and the crossing number of C7× Cn

Journal of Combinatorial Theory Series B
An Improved Bound for the Crossing Number of CmCn: a Self–Contained Proof Using Mostly Combinatorial Arguments

Graphs and Combinatorics
Crossing number is hard for cubic graphs

Journal of Combinatorial Theory Series B
An Upper Bound for the Bisection Width of a Diagonal Mesh

IEEE Transactions on Computers
Bounding the crossing number of a graph in terms of the crossing number of a minor with small maximum degree

Journal of Graph Theory
The crossing number of Cm × Cn is as conjectured for n ≥ m(m + 1)

Journal of Graph Theory
Universality considerations in VLSI circuits

IEEE Transactions on Computers
A counterexample to Tang and Padubidri's claim about the bisection width of a diagonal mesh

IEEE Transactions on Computers

Quantified Score

Hi-index	0.00

Visualization

Abstract

An orthogonal drawing of a graph is an embedding of the graph in the plane such that each edge is representable as a chain of alternately horizontal and vertical line segments. This style of drawing finds applications in areas such as optoelectronic systems, information visualization and VLSI circuits. We present orthogonal drawings of the Kronecker product of two cycles around vertex partitions of the graph into grids. In the process, we derive upper bounds on the crossing number of the graph. The resulting upper bounds are within a constant multiple of the lower bounds. Unlike the Cartesian product that is amenable to an inductive treatment, the Kronecker product entails a case-to-case analysis since the results depend heavily on the parameters corresponding to the lengths of the two cycles.