Euler index in uncertain graph

As the system becomes more complex, in practical application of graph theory, different types of uncertainty are frequently encountered. In an uncertain graph, whether two vertices of the graph are joined cannot be completely determined. Within the framework of uncertainty theory, the concept of Euler index of uncertain graph is proposed. A method to calculate Euler index of uncertain graph is also given. What’s more, the Euler index of uncertain cycle and uncertain graph with blocks can be obtained in a simple way.

► The concept of Euler index of uncertain graph is proposed.
► It gives a method to calculate Euler index of uncertain graph.
► The Euler index of uncertain cycle and uncertain graph with blocks can be obtained in a simple way.