On k-graceful labeling of pendant edge extension of complete bipartite graphs

• Published in: Algebra and Discrete Mathematics
• Date: 2018
• Main Authors: Bhoumik, S., Mitra, S.
• Format: Article
• Language: English
• Published: Інститут прикладної математики і механіки НАН України 2018
• Online Access: https://nasplib.isofts.kiev.ua/handle/123456789/188358
• Journal Title: Digital Library of Periodicals of National Academy of Sciences of Ukraine
• Cite this: On k-graceful labeling of pendant edge extension of complete bipartite graphs / S. Bhoumik, S. Mitra // Algebra and Discrete Mathematics. — 2018. — Vol. 25, № 2. — С. 188–199. — Бібліогр.: 14 назв. — англ.

For any two positive integers m, n, we denote the graph Km,n ⊙ K₁ by G. Ma Ke-Jie proposed a conjecture [9] that pendant edge extension of a complete bipartite graph is a k-graceful graph for k > 2. In this paper we prove his conjecture for n ≤ m < n² + ⎣k/n⎦ + r.