Questions tagged [combinatorics]

For questions about the study of finite or countable discrete structures, especially how to count or enumerate elements in a set (perhaps of all possibilities) or any subset. It includes questions on permutations, combinations, bijective proofs, and generating functions.

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A small help needed in proving a smart part of a result - to show that we need at least 2r-3 vertices to construct a particular type of graph.

I am given a graph $G$ with diameter two. I have to prove that I have to add minimum $2r-3$ vertices to $G$ to form a graph $H$ such that $H$ contains exactly two vertices with eccentricity $r+1$ (...