Ball number — шаровое число (графа).
By a family of solid balls in , we mean a family of balls no two of which penetrate each other. A chain is a finite sequence of solid balls in which each consecutive pair of balls is tangent. The two balls are called the end balls of the chain.
Let be two solid balls. If an end of a chain is tangent to , and the other end of the chain is tangent to , then the chain is said to connect . Let be a finite graph. Take a family of red solid balls . Connect each non-tangent pair () by a chain of blue solid balls so that no two distinct chains share a blue ball. Then we have a family consisting of solid balls , and the solid balls making the chains. This family is called a representation of . The ball number of is the minimum number of balls necessary to make a representation of . For example, , .
- Евстигнеев В.А., Касьянов В.Н. Словарь по графам в информатике. — Новосибирск: Сибирское Научное Издательство, 2009.