On Super Heronian Mean Labeling of Some Subdivision Graphs

Authors

  • Lorelie S. Valencerina Department of Mathematics and Statistics, University of Southeastern Philippines, Davao City, Philippines
  • Ariel C. Pedrano Department of Mathematics and Statistics, University of Southeastern Philippines, Davao City, Philippines https://orcid.org/0000-0003-0545-2121

DOI:

https://doi.org/10.26713/cma.v15i2.2162

Keywords:

Super Heronian mean graph, Subdivision graph, Snake graphs

Abstract

Let \(f:V(G) \rightarrow \{1, 2, \dots, p+q \}\) be an injective function, where \(p=|V(G)|\) and \(q=|E(G)|\). For a vertex labeling \(f\) the induced edge labeling \(f^*(e=uv)\) is defined by,
\[
f^*(e)= \left \lfloor {\frac{f(u)+\sqrt{f(u)f(v)}+f(v)}{3}} \right \rfloor \ \text{or} \ \left \lceil\frac{f(u)+\sqrt{f(u)f(v)}+f(v)}{3} \right \rceil.
\]
Then \(f\) is called a super Heronian mean labeling if \(\{f(V(G))\} \cup \{f(e): e \in E(G)\}=\{1, 2, 3, \dots, p+q\}\). A graph which admits super Heronian mean labeling is called super Heronian mean graph.

Downloads

Download data is not yet available.

References

J. A. Gallian, A dynamic survey of a graph labeling, The Electronic Journal of Combinatorics (Dynamic Survey), Version 25 (2016), 623 pages, URL: 10.37236/27.

N. Revathi, Mean labeling of some graphs, International Journal of Science and Research 4 (2015), 1921 – 1923.

S. S. Sandhya, E. E. R. Merly and G. D. Jemi, Some results on super Heronian mean labeling of graphs, International Journal of Contemporary Mathematical Sciences 11 (10) (2016), 485 – 495, DOI: 10.12988/ijcms.2016.6843.

S. S. Sandhya, E. E. R. Merly and G. D. Jemi, Some more results on super heronian mean labeling, International Journal of Mathematics Research 8(3) (2016), 199 – 206.

S. S. Sandhya, E. E. R. Merly and G. D. Jemi, Some new results on super Heronian mean, Journal of Mathematics Research 9(1) (2017), 62 – 67, DOI: 10.5539/jmr.v9n1p62.

S. S. Sandhya, E. E. R. Merly and G. D. Jemi, On super Heronian mean labeling of graphs, Asia Pacific Journal of Research 1 (2017), 127 – 133, DOI: 10.12988/IMF.2017.68108.

Downloads

Published

14-11-2024
CITATION

How to Cite

Valencerina, L. S., & Pedrano, A. C. (2024). On Super Heronian Mean Labeling of Some Subdivision Graphs. Communications in Mathematics and Applications, 15(2), 597–603. https://doi.org/10.26713/cma.v15i2.2162

Issue

Vol. 15 No. 2 (2024)

Section

Research Article

License

Creative Commons Licence 4.0 by  

Authors who publish with this journal agree to the following terms:

  • Authors retain copyright and grant the journal right of first publication with the work simultaneously licensed under a CCAL that allows others to share the work with an acknowledgement of the work's authorship and initial publication in this journal.
  • Authors are able to enter into separate, additional contractual arrangements for the non-exclusive distribution of the journal's published version of the work (e.g., post it to an institutional repository or publish it in a book), with an acknowledgement of its initial publication in this journal.
  • Authors are permitted and encouraged to post their work online (e.g., in institutional repositories or on their website) prior to and during the submission process, as it can lead to productive exchanges, as well as earlier and greater citation of published work.