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

• Видавець: Lugansk National Taras Shevchenko University
• Дата: 2018
• Автори: Bhoumik, Soumya, Mitra, Sarbari
• Формат: Стаття
• Мова: English
• Опубліковано: Lugansk National Taras Shevchenko University 2018
• Теми: \(k\)-graceful labeling; complete bipartite graph; corona; \(1\)-crown; 05C78
• Онлайн доступ: https://admjournal.luguniv.edu.ua/index.php/adm/article/view/224

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...