Math Problem Statement
Show that if G is a non-regular graph of order n and size rn/2 for some integer r with 1 ≤ r ≤ n − 2, then ∆(G) − δ(G) ≥ 2.
Solution
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Math Problem Analysis
Mathematical Concepts
Graph Theory
Degree of a Vertex
Non-Regular Graphs
Formulas
Degree sum formula: \( \sum_{v \in V(G)} \deg(v) = 2m \)
Theorems
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Suitable Grade Level
Undergraduate Level
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