Polygonal Graceful Labeling of Some Simple Graphs

Authors

  • A Rama Lakshmi Research Scholar (Part time-Internal), Department of Mathematics, The M.D.T Hindu college, Affiliated to Manonmaniam Sundaranar University, Tirunelveli–627010, Tamil Nadu, India.
  • M P Syed Ali Nisaya Assistant Professor, Department of Mathematics, The M.D.T Hindu college, Affiliated to Manonmaniam Sundaranar University, Tirunelveli–627010, Tamil Nadu, India.

DOI:

https://doi.org/10.23755/rm.v44i0.883

Keywords:

Polygonal numbers, Polygonal graceful labeling, Polygonal graceful graph

Abstract

Let  be a graph with vertices and edges.  Let andbe the vertex set and edge set of respectively.  A polygonal graceful labeling of a graph  is an injective function , where  is a set of all non-negative integers that induces a bijection , where  is the  polygonal number such that for every edge .  A graph which admits such labeling is called a polygonal graceful graph. For , the above labeling gives triangular graceful labeling. For , the above labeling gives tetragonal graceful labeling and so on. In this paper, polygonal graceful labeling is introduced and polygonal graceful labeling of some simple graphs is studied

References

M. Apostal, Introduction to Analytic Number Theory, Narosa Publishing House, Second Edition – (1991).

FrankHarary, Graph Theory, Narosa Publishing House – (2001).

J.A. Gallian, A Dynamic Survey of Graph Labeling, The Electronic Journal of Combinatorics, 16(2013), #DS6.

S.W. Golomb, How to number a graph, Graph Theory and Computing, R.C.Read, Academic Press, New York (1972), 23-37.

D.S.T. Ramesh and M.P. Syed Ali Nisaya, Some More Polygonal Graceful Labeling of Path, International Journal of Imaging Science and Engineering, Vol. 6 , No.1 , January 2014, 901-905.

A. Rosa, On Certain Valuations of the vertices of a graph, Theory of Graphs, (Proc. InternetSymposium,Rome,1966, Gordon and Breach N.Y. and Dunod Paris (1967), 349-355.

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Published

2022-12-11

Issue

Vol. 44 (2022): Special Issue: Recent Trends in Mathematics and its Applications

Section

Volume 45-2023

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