Cordial Labeling of the Line Graph of Bistar

Authors

  • M. I. Bosmia Department of Mathematics, Government Engineering College, Bharuch 392001, Gujarat, India https://orcid.org/0000-0001-7781-2638
  • M. A. Patel Department of Mathematics, Government Engineering College, Modasa 383315, Gujarat, India https://orcid.org/0000-0002-5932-0303
  • Y. M. Parmar Department of Mathematics, Government Engineering College, Gandhinagar 382028, Gujarat, India
  • P. L. Vihol Department of Mathematics, Vishwakarma Government Engineering College, Ahmedabad 382424, Gujarat, India https://orcid.org/0000-0002-1645-8206

DOI:

https://doi.org/10.26713/cma.v16i3.3317

Keywords:

Line graph, Bistar, Cordial labeling

Abstract

A binary vertex labeling \(f\) of a graph \(G\) is called a cordial labeling if \(|v_f(0)-v_f(1)| \leq 1\) and \(|e_f(0)-e_f(1)| \leq 1\). A graph which admits cordial labeling is called a cordial graph. In this paper, the necessary and sufficient conditions for the line graph of bistar \(B_{n,p}\) to be cordial when \(p=n+4m\) and \(p=n+4m+2\) where \(m\in \mathbb{N}\cup \{0\}\) are discussed.

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References

M. I. Bosmia and K. K. Kanani, Various graph labeling techniques for the line graph of Bistar, International Journal of Technical Innovation in Modern Engineering & Science 4(09) (2018), 851 – 858.

D. M. Burton, Elementary Number Theory, 7th edition, McGraw-Hill Publisher, New York, xii + 436 pages (2011).

I. Cahit, Cordial Graphs: A weaker version of graceful and harmonious graphs, Ars Combinatoria, 23 (1987), 201 – 208.

J. A. Gallian, A dynamic survey of graph labeling, The Electronic Journal of Combinatorics 25 (2022), # DS6, URL: https://www.combinatorics.org/files/Surveys/ds6/ds6v25-2022.pdf.

J. L. Gross and J. Yellen, Graph Theory and Its Applications, 2nd edition, Chapman and Hall/CRC, New York, 800 pages (2005), DOI: 10.1201/9781420057140.

F. Harary and R. Z. Norman, Some properties of line digraphs, Rendiconti del Circolo Matematico di Palermo 9 (1960), 161 – 168, DOI: 10.1007/BF02854581.

D. Kuo, G. J. Chang and Y. H. H. Kwong, Cordial labeling of mKn, Discrete Mathematics 169(1-3) (1997), 121 – 131, DOI: 10.1016/S0012-365X(95)00336-U.

S. K. Vaidya and C. M. Barasara, Product cordial labeling of line graph of some graphs, Kragujevac Journal of Mathematics 40(2) (2016), 290 – 297.

S. K. Vaidya and N. H. Shah, Cordial labeling of some bistar related graphs, International Journal of Mathematics and Soft computing 4(2) (2014), 33 – 39.

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Published

30-10-2025
CITATION

How to Cite

Bosmia, M. I., Patel, M. A., Parmar, Y. M., & Vihol, P. L. (2025). Cordial Labeling of the Line Graph of Bistar. Communications in Mathematics and Applications, 16(3), 895–907. https://doi.org/10.26713/cma.v16i3.3317

Issue

Vol. 16 No. 3 (2025)

Section

Research Article

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