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

• Date: 2018
• Main Authors: Bhoumik, Soumya, Mitra, Sarbari
• Format: Article
• Language: English
• Published: Lugansk National Taras Shevchenko University 2018
• Subjects: \(k\)-graceful labeling; complete bipartite graph; corona; \(1\)-crown; 05C78
• Online Access: https://admjournal.luguniv.edu.ua/index.php/adm/article/view/224
• Journal Title: Algebra and Discrete Mathematics

For any two positive integers \(m,n\), we denote the graph \(K_{m,n}\odot K_1\) by \(G\). Ma Ke-Jie proposed a conjecture [9] that pendant edge extension of a complete bipartite graph is a \(k\)-graceful graph for \(k \ge 2\). In this paper we prove his conjecture for \(n\le m < n^2+\lfloor\f...