Euler index of uncertain random graph: concepts and properties

ABSTRACT

We are usually in the state of indeterminacy. Uncertainty and randomness are two basic types of indeterminacy. In many cases, uncertainty and randomness exist simultaneously in a complex system. This paper considers the Euler tour of an uncertain random graph, in which some edges exist with some degrees in uncertain measure and others exist with some degrees in probability measure. In order to show how likely an uncertain random graph is Eulerian, an Euler index of an uncertain random graph is proposed first. Then a method to calculate the Euler index of an uncertain random graph is given. In addition, some properties of the Euler index are discussed.

KEYWORDS:

• Uncertainty theory
• chance theory
• uncertain random variable
• uncertain random graph
• Euler index

2010 AMS SUBJECT CLASSIFICATIONS:

• 05C99
• 68R99

Disclosure statement

No potential conflict of interest was reported by the author(s).