Graceful and residually graceful graphs

• Main Author: Tan, Michele Go
• Format: text
• Language: English
• Published: Animo Repository 2006
• Subjects: Graph theory; Mathematics
• Online Access: https://animorepository.dlsu.edu.ph/etd_masteral/3399; https://animorepository.dlsu.edu.ph/context/etd_masteral/article/10237/viewcontent/CDTG004077_P.pdf
• Institution: De La Salle University

Graph labeling is an assignment of integers to the vertices and/or edges of a graph, subject to certain conditions. The first type of labeling was introduced by Rosa as early as 1967. It is called -valuation and, more popularly known as graceful labeling from which other types of labeling arose. In 1982 Bloom and Hsu extended the concepts of graceful graphs to digraphs. In a paper of Gervacio in 1999, the concept of residually graceful digraphs was introduced. In this thesis, results from the papers of Gervacio entitled On Graceful, Residually Graceful and Properly Graceful Digraphs and Residually Graceful Orientations of Graphs will be discussed and illustrated. Graceful and residually graceful labeling of some special types of graphs such as star and starpath are also discussed. Further several conjectures regarding gracefulness of particular graphs are presented in this paper.