A Study about Continuous Edge Coloring for K_n Complete Graph
Abstract
As it’s known, The Graph k-Colorability Problem (GCP) is a well-known NP-Hard Problem. This problem consists in finding the k minimum number of colors to color the vertices of a graph in such a way that any two adjacent vertices, which are connected by an edge, have always different colors. In another words how can we color the edges of a graph in such a way that any two edges joined by a vertex have always different colors. In this paper we consider a new type of coloring is the Continuous Edge Coloring (CEC), and we introduce a new effective algorithm for continuous edge coloring of the complete graph , we also determine the chromatic number of continuous edge coloring accurately. The proposed algorithm allows achieving a Continuous Edge Coloring for a set of Complete Graphs when the number of vertices is even. This algorithm was implemented in the virtual programming language Delphi. Actually we develop two programs: the first one is supporting Windows platform, the second one is available for smart phones users, where it supports Android platform.
Downloads
Published
How to Cite
Issue
Section
License
This work is licensed under a Creative Commons Attribution-NonCommercial-ShareAlike 4.0 International License.
The authors retain the copyright and grant the right to publish in the magazine for the first time with the transfer of the commercial right to the Tishreen University Journal -Basic Sciences Series
Under a CC BY- NC-SA 04 license that allows others to share the work with of the work's authorship and initial publication in this journal. Authors can use a copy of their articles in their scientific activity, and on their scientific websites, provided that the place of publication is indicted in Tishreen University Journal -Basic Sciences Series . The Readers have the right to send, print and subscribe to the initial version of the article, and the title of Tishreen University Journal -Basic Sciences Series Publisher
journal uses a CC BY-NC-SA license which mean
You are free to:
- Share — copy and redistribute the material in any medium or format
- Adapt — remix, transform, and build upon the material
- The licensor cannot revoke these freedoms as long as you follow the license terms.
- Attribution — You must give appropriate credit, provide a link to the license, and indicate if changes were made. You may do so in any reasonable manner, but not in any way that suggests the licensor endorses you or your use.
- NonCommercial — You may not use the material for commercial purposes.
- ShareAlike — If you remix, transform, or build upon the material, you must distribute your contributions under the same license as the original.
- No additional restrictions — You may not apply legal terms or technological measures that legally restrict others from doing anything the license permits.