Draft:Lambda function (graph theory)

• Comment: This title and this draft are purely promotional for junk research defining and renaming binomial coefficients, a concept that has been well known for millenia. —David Eppstein (talk) 22:43, 24 March 2024 (UTC)

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In a generalised form of graph theory, the lambda function of a nonnegative integer $n$, notated as $\lambda (n)$ or $\lambda n$, is equal to the exact number of links required so that there is not a single entity of entities that is not directly connected by a single link per connection to every other entity of entities. This means that it is equal to the number of edges in $K_{n}$, the complete graph of $n$ vertices, in graph theory.

The lambda function was introduced in the 2024 generalised graph theory paper "The lambda function - computing required amounts of links to make every one of a number of entities directly linked to each other" by the mathematician Charles Ewan Milner.

In his paper, Milner gives these formulas for values of the lambda function which are valid only when all the variables are nonnegative integers: $\lambda (n)=\lambda (n-1)+n-1$, $\lambda (a+b)=\lambda (a)+\lambda (b)+ab$, and $\lambda (a+b+c)=\lambda (a)+\lambda (b)+\lambda (c)+ab+bc+ac$.