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学者姓名：王小霖
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A graph G is diameter-2-critical if its diameter is 2, and the deletion of any edge strictly increases the diameter. The longstanding Murty-Simon Conjecture states that for any diameter-2-critical graph G of order n, e(G) <= left perpendicular n(2)/4 right perpendicular and the unique extremal graph is K-inverted right perpendicular n/2 inverted left perpendicular,K- left perpendicular n/2 right perpendicular. After more than ten years, Furedi (JGT,1992) confirmed the Murty-Simon Conjecture for sufficiently large n. In the same paper, Furedi claimed (without proof) that all diameter-2-critical graphs with at least left perpendicular (n-1)(2)/ 4 right perpendicular +1 edges are complete bipartite graphs and M, where M is obtained by subdividing one edge of K-inverted right perpendicular ((n-1)/2 inverted left perpendicular, left perpendicular (n-1)/2 right perpendicula). Later, Balbuena, Hansberg, Haynes, and Henning (Graphs Combin., 2015) presented a class of diameter-2-critical graphs containing M. And all of them have left perpendicular (n-1)(2)/ 4 right perpendicular +1 edges. So Furedi's claim needs to be revised. In this paper, we prove that all C5-free diameter2-critical graphs with at least left perpendicular (n-1)(2)/ 4 right perpendicular +1 + 1 edges are complete bipartite graphs for sufficiently large n. (c) 2025 Elsevier B.V. All rights are reserved, including those for text and data mining, AI training, and similar technologies.
Keyword ：
C-5-free C-5-free Complete bipartite graph Complete bipartite graph Diameter-2-critical Diameter-2-critical
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| GB/T 7714 | Lin, Qiao , Wang, Xiaolin . Characterize all C5-free diameter-2-critical graphs with at least inverted left perpendicular (n-1)2/4 inverted right perpendicular+1 edges [J]. | DISCRETE APPLIED MATHEMATICS , 2025 , 375 : 332-337 . |
| MLA | Lin, Qiao 等. "Characterize all C5-free diameter-2-critical graphs with at least inverted left perpendicular (n-1)2/4 inverted right perpendicular+1 edges" . | DISCRETE APPLIED MATHEMATICS 375 (2025) : 332-337 . |
| APA | Lin, Qiao , Wang, Xiaolin . Characterize all C5-free diameter-2-critical graphs with at least inverted left perpendicular (n-1)2/4 inverted right perpendicular+1 edges . | DISCRETE APPLIED MATHEMATICS , 2025 , 375 , 332-337 . |
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