(untitled) (Latakia University Journal -Basic Sciences Series, 2021)
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.