Isnaini Rosyida, Widodo, Ch. Rini Indrati, Kiki A. Sugeng
A graph is called an edge uncertain graph if the edges are not deterministic but exist with some belief degrees described by uncertain measure. A new definition for total uncertain graph is first introduced in this paper, that is an uncertain graph in which the vertices and the edges are not deterministic. Further, we give a concept of an α-cut of a total uncertain graph and investigate some of its properties. We color a total uncertain graph via the α-cut, and obtain α-cut chromatic numbers for all α ∈ [0, 1]. Some properties of the α-cut chromatic number are also verified. © 2016 AIP Publishing LLC.
Department of Mathematics, Gadjah Mada University, Indonesia; Department of Mathematics, Semarang State University, Indonesia; Dept of Mathematics, University of Indonesia, Indonesia
