Vol. 25 No. 1 (2026): Mapana Journal of Sciences
Research Articles

Some Results on Square Prime Cordial Graphs

I. Blessy
Department of Mathematics and Research Centre, Sarah Tucker College, Affiliated to Manonmaniam Sundaranar University, Tirunelveli, Tamil Nadu, India
I. Gnanaselvi
Department of Mathematics and Research Centre, Sarah Tucker College, Affiliated to Manonmaniam Sundaranar University, Tirunelveli, Tamil Nadu, India

Published 2026-02-19

Keywords

  • SPC labeling,
  • SPC graph,
  • parity labeling

Abstract

Let G = (p, q) be a graph with p vertices and q edges. A SPC labeling of a graph G with vertex collection V(G) is a bijection alpha: V(G) --> {0, 1, 2, .... p-1} to be the extent that its induced binary edge labeling function alpha*: E(G) --> {0,1} is defined by alpha*(uv) = 

The difference between the edges designated as 0, denoted by ealpha(0) and the edges designated as 1, denoted by ealpha(1) is atmost 1. A graph which follows SPC labeling is referred to as SPC graph.  This paper elucidates that broom graph Bn,m and K1,m * K1,n admits SPC labeling and some results.

References

  1. J. A. Gallian, A dynamic survey of graph labeling. The Electronics Journal of Combinatornics, (2024), # Ds6, 1-712.
  2. F. Harary Graph Theory Narosa Publishing House, New Delhi, 1988.
  3. S Dhanalakshmi and N. Parvathi 2019 J. Phys.: Conf. Ser. 1377 012027. DOI:10.1088/1742-6596/1377/1/012027.
  4. Parul B Pandya, N P Shrimali, Vertex-Edge Neighborhood Prime Labeling of Some Graphs., Volume 7, Issue 10, 2018, ISSN NO:2279-543X, Page No. 735-743.
  5. Arockiam, Lourdusamy & F, Patrick. (2016). Sum divisor cordial graphs. Proyecciones. 35. 119-136. 10.4067/S0716-09172016000100008.
  6. S. Stanly, I. Gnanaselvi, S.Alice Pappa, Mean Square Difference Cordial Labeling of Path Related Graphs, International Journal of Food and Nutritional Sciences, ISSN: 2320 7876/ 2022, Issue: 11, Pages: 16554 – 16573.
  7. S. Stanly, I. Gnanaselvi, S. Alice Pappa, Mean Square Difference Cordial Labeling of Some Graphs, Design Engineering, ISSN: 0011-9342/ year 2021, Issue: 9, Pages: 5108-5115.
  8. S. Dhanalakshmi and N Parvathi, (2018) Journal of Physics Conference Series 2516, 210013 (2022). DOI: 10.1063/5.0109630
  9. Dr. A. Sugumaran and P. Vishnu Prakash. Some new results of Prime Cordial Labeling. International J. of Pure & Engg. Mathematics (IJPEM) ISSN 2348-3881, Vol. 5 No. I (April, 2017), pp. 9-14.
  10. M. Sundaram, R. Ponraj and S. Somasundaram, Prime cordial labeling of graphs, Journal of Indian Academy of Mathematics, 27(2005) 373-390.
  11. I. Cahit, Cordial graph A weaker version of graceful and harmonious graphs, Ars Combinatoria, 23(1987), 201-207.
  12. A. Rosa, (1967) On Certain Valuations of the vertices of a graph, in Theory of Graphs, International Symposium, Rome, July 1966, Gordon and Breach, New York and Dunod, Paris, pp.349-355.
  13. Ru, Min. "Greatest Common Divisors." University of Houston, spring 2011.
  14. K. Gayathri, A. Sasikala, C. Sekar, (2021) Journal of Physics Conference Series 1947 012016. DOI: 10.1088/1742-6596/1947/1/012016