An a-Cut Chromatic Number of a Total Uncertain Graph and Its Properties

摘要

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 a-cut of a total uncertain graph and investigate some of its properties. We color a total uncertain graph via the a-cut, and obtain a-cut chromatic numbers for all α ∈ [0,1]. Some properties of the α-cut chromatic number are also verified.