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Tight Super-Edge-Graceful Labelings of Trees and Their Applications
AKCE International Journal of Graphs and Combinatorics
  • Alex Collins, Georgia State University
  • Colton Magnant, Georgia Southern University
  • Hua Wang, Georgia Southern University
Document Type
Article
Publication Date
11-1-2015
DOI
10.1016/j.akcej.2015.11.004
Disciplines
Abstract

The concept of graceful labeling of graphs has been extensively studied. In 1994, Mitchem and Simoson introduced a stronger concept called super-edge-graceful labeling for some classes of graphs. Among many other interesting pioneering results, Mitchem and Simoson provided a simple but powerful recursive way of constructing super-edge-graceful trees of odd order. In this note, we present a stronger concept of “tight” super-edge-graceful labeling. Such a super-edge graceful labeling has an additional constraint on the edge and vertices with the largest and smallest labels. This concept enables us to recursively construct tight super-edge-graceful trees of any order. As applications, we provide insights on the characterization of super-edge-graceful trees of diameter 4, a question posed by Chung, Lee, Gao and Schaffer. We also observe infinite families of super-edge-graceful trees that can be generated from tight labelings. Given the direct applications of “tight” super-edge-graceful labeling to the study of super-edge-graceful labelings, we note that it is worthwhile to further examine recursively generated tight super-edge-graceful trees.

Comments

© 2015 Kalasalingam University. Production and Hosting by Elsevier B.V. This is an open access article under the CC BY-NC-ND license (http://creativecommons.org/licenses/by-nc-nd/4.0/). This article was retrieved from the AKCE International Journal of Graphs and Combinatorics.

Citation Information
Alex Collins, Colton Magnant and Hua Wang. "Tight Super-Edge-Graceful Labelings of Trees and Their Applications" AKCE International Journal of Graphs and Combinatorics Vol. 12 Iss. 2-3 (2015) p. 113 - 118 ISSN: 0972-8600
Available at: http://works.bepress.com/colton_magnant/61/