journal-of-discrete-mathematical-sciences-and-cryptography Journal of Discrete Mathematical Sciences and Cryptography 2169-0065 0972-0529 Taru Publications 10.47974/JDMSC-1722 On k-super graceful graphs with extremal maximum vertex degree Lau Gee-Choon College of Computing, Informatics & Mathematics, Universiti Teknologi MARA, Johor Branch, Segamat Campus, 85000, Malaysia Shiu Wai Chee Department of Mathematics, The Chinese University of Hong Kong, Shatin, Hong Kong, P.R. China Ng Ho-Kuen Department of Mathematics, San José State University, San Jose, CA, 95192, U.S.A. Gao Zhen-Bin College of Mathematical Sciences, Harbin Engineering University, Harbin, 150001, P.R. China Schaffer Karl Department of Mathematics, De Anza College, Cupertino, CA, 95014, U.S.A. 27 6 1765 1783 16 09 2024

Let G(V, E) be a simple and loopless graph with |V|  vertices and |E|  edges. For k ≥ 1,  a graph G is called k-super graceful if there is a bijective labeling f : V ∪ E → {i | k ≤ i ≤ k + |V| + |E| – 1} with f(vu) = |f(v) – f(u)|  for every edge uv ∈ E.  In this paper, we study the existence of k-super graceful labeling of certain graphs with extremal maximum vertex degree.

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