Crossing Number of Infinite Family of Extension Kochol's Periodic Graphs

Abstract

At this time, technology is developing very quickly and is increasingly sophisticated. This technological development is certainly closely related to the development of computer technology. A computer is able to control a series of electronic devices using an IC chip that can be filled with programs and logic called microprocessor technology. A microprocessor is a digital component of the VLSI (Very Large Scale Integration) type with very high circuit complexity that is capable of carrying out the functions of a CPU (Central Processing Unit). Among many applications, the problem of crossing number very interesting and important because of its application in the optimization of chip are required in a circuit layout of VLSI. Crossing number used to obtain the lower bound on the amount of chip area of VLSI devices like microprocessor and memory chips additionally, crossings in the circuit layout could cause short circuit and therefore worth minimized independent of the chip area consideration. Some graph can be seen as built by small pieces. A principal tool used in construction of crossing-critical graphs are tiles. In the tile concept, tiles can be arranged by gluing one tile to another in a linear or circular fashion. The series of tiles with circular fashion form an infinite graph family. In this way, the intersection number of this family of graphs can be determined. In this research, has been formed an infinite family graphs The graph formed by gluing together many copies of the tile  in circular fashion, where the tile  consists of identical tile sections. The results obtained show that the graph  has 3-crossing-critical of a graph.