Odd Graceful Labelings of Prism Graphs

N. Bradley Fox; Briauna Bonney; Sage Patten

doi:10.33043/yga37vtyebt

Authors

N. Bradley Fox Austin Peay State University
Briauna Bonney Middle College at Austin Peay State University
Sage Patten Middle College at Austin Peay State University

DOI:

https://doi.org/10.33043/yga37vtyebt

Abstract

Odd graceful labelings of a graph are a variation of a graceful labeling. In each, the vertices are uniquely labeled with integers, and edges are assigned the difference between the incident vertex labels. For a graph with m edges, the goal of a graceful labeling is to have distinct edge labels 1 to m, while an odd graceful labeling has odd edge labels from 1 to 2m−1. In this paper we construct odd graceful labelings of prism graphs, denoted C_n×P₂, when n is even using the cases of n = 6k,6k+2, and 6k+4, which require similar but altered labelings.

Author Biographies

N. Bradley Fox, Austin Peay State University

N. Bradley Fox is a Professor of Mathematics at Austin Peay State University. He earned his Ph.D. in Mathematics at the University of Kentucky in 2015. His research interests focus within graph theory, particularly graph labelings and colorings, while also working on projects relating to gerrymandering and voting theory.

Briauna Bonney, Middle College at Austin Peay State University

Briauna Bonney contributed to this paper during her junior and senior years while attending Middle College at Austin Peay State University. She earned her associate's degree and high school diploma in May 2025, and is pursuing a Bachelor of Science in Engineering at the University of Tennessee, Knoxville in the fall.

Sage Patten, Middle College at Austin Peay State University

Sage Patten graduated from Middle College at Austin Peay State University, where she contributed to this research paper during her junior and senior years of high school. Since earning her associate's degree, she has been pursuing a Bachelor of Fine Arts in Architecture with a minor in Environmental Studies at the University of Memphis, driven by a desire to blend artistic expression with mathematical principles.

References

L. Brankovic, I. Wanless, Graceful Labeling: State of the Art, Applications, and Future Directions, Math. in Comp. Sci., 5 (2011), 11–20.

R. Frucht, Graceful Numbering of Wheels and Related Graphs, Ann. New York Acad. Sci., 319 (1979), 219–229.

R. Frucht, J.A. Gallian, Labeling Prisms, Ars Combin., 26 (1988). 69–82.

J. Gallian, A Dynamic Survey of Graph Labeling, Electron. J. Comb., DS06 (1996), 1–389.

R. B. Gnanajothi, Topics in Graph Theory, Ph.D. Thesis, Madurai Kamaraj University, (1991).

S. Golomb, How to Number a Graph, in Graph Theory and Computing, R. C. Read, ed., Academic Press, New York (1972), 23–37.

A. Graf, Graceful Labelings of Pendant Graphs, Rose-Hulman Undergrad. Math. J., 15 No. 1 (2014), Article 10.

J. Huang and S. Skiena, Gracefully Labeling Prisms, Ars Combin., 38 (1994), 225–242.

D. Jungreis and M. Reid, Labeling Grids, Ars Combin., 34 (1992), 167–182.

R. Montgomery, A. Pokrovskiy, and B. Sudakov, A Proof of Ringel's Conjecture, Geom. Funct. Anal., 31 (2021), 663–720.

G. Ringel, Theory of Graphs and its Applications, Proceedings of the Symposium Smolenice (1963).

A. Rosa, On Certain Valuations of the Vertices of a Graph, Theory of Graphs (Internat. Symposium, Rome, July 1966), Gordon and Breach, N. Y. and Dunod Paris (1967), 349-355.

Q. T. Yan, Odd Gracefulness and Odd Strongly Harmoniousness of the Product Graphs P n ×Pm, J. Syst. Sci. Math. Sci., 30 (2010), 341–348.

Odd Graceful Labelings of Prism Graphs

Authors

DOI:

Abstract

Author Biographies

N. Bradley Fox, Austin Peay State University

Briauna Bonney, Middle College at Austin Peay State University

Sage Patten, Middle College at Austin Peay State University

References

Downloads

Published

How to Cite

Issue

Section

License