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Slope Number on Complete Graphs
Objective: A straight line drawing is a mapping of an edge into a straight line segment. The minimum number of distinct slopes used in a straight line drawing of a graph G is called the slope number of the graph G. In this paper the slope number of complete graph is studied elaborately. Methods: This optimization problem is NP-Hard for any arbitrary graph. A canonical way of drawing of a complete graph is an existing one. In present paper, we consider the edges of a complete graph are straight line segments in order to obtain the number of slopes. Findings: This paper interprets the characterization of slopes in complete graph according to an odd and even number of edges and investigated in detail. Moreover, the slope number of a complete graph is compared with the chromatic number of complete graph and the results are observed. Applications/Improvement: Slope number is one of the quality measures of graph drawing. It is used to find out different layout methods for the same graph.
Chromatic Number, Complete Bipartite Graph, Complete Graph, Slope Number, Straight Line Drawing.
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