On graceful graphs

• Main Authors: Paculba, Marianne S., Tan-Gatue, Christine B.
• Format: text
• Language: English
• Published: Animo Repository 1998
• Subjects: Graph theory; Paths and cycles (Graph theory); Trees (Graph theory); Programming (Mathematics); Algorithms
• Online Access: https://animorepository.dlsu.edu.ph/etd_bachelors/16428
• Institution: De La Salle University

This paper presents a pattern of labeling for some special graceful graphs like paths, cycles, complete graphs, complete bipartite graphs and some trees. It also contains a mouse-driven computer program written in C programming language to handle the labeling for more general graceful graphs. Aside from computer programming, this paper is mostly expository in nature. Other findings included in this paper were results from graph addition, graph complementation and subgraph formation. Illustrations were provided to show that the complement of graceful (or non-graceful) graphs need not be graceful (or non-graceful). The same is true for the subgraphs of graceful (or non-graceful) graphs. In graph addition, adding two graceful graphs (or two non-graceful graphs or a graceful and a non-graceful graph) will yield to either a graceful or a non-graceful graph. As a conclusion, performing these graph operations on both graceful and non-graceful graphs does not guarantee the gracefulness and the non-gracefulness of the resulting graph/s. Also, it shows that graceful graphs need not have a unique graceful labeling.