Skolem Odd Vertex Graceful Signed Graphs
for Star Graph

P. Shalini

doi:https://doi.org/10.14445/22315373/IJMTT-V69I8P504

International Journal of Mathematics Trends and Technology

Research Article | Open Access | Download PDF

Volume 69 | Issue 8 | Year 2023 | Article Id. IJMTT-V69I8P504 | DOI : https://doi.org/10.14445/22315373/IJMTT-V69I8P504

Skolem Odd Vertex Graceful Signed Graphs for Star Graph

P. Shalini

Received	Revised	Accepted	Published
10 Jun 2023	26 Jul 2023	08 Aug 2023	24 Aug 2023

Abstract

In this article, skolem odd vertex graceful signed graphs on directed graphs have been introduced. A graph G(P, m, n) is a bijective function f:V(G) → {1, 3, 5, 7, …, 2p-1} such that, when each edge uv E(G) is assigned by f(uv) = f(v) – f(u) the positive edges receive distinct labels from the set {1, 3, 5, …, 2m-1} and the negative edges receive distinct labels from the set {-1, -3, -5, -7, ..., -2n-1}, it is called as a skolem odd vertex graceful signed graphs. In this article, star graph is investigated under skolem odd vertex graceful labeling for signed graph.

Keywords

Graceful labeling, Signed graphs, Additive labeling, Skolem edge graceful labeling.

References

[1] J. AmalorpavaJerline et al., “F-Index of Generalized Mycielskian Graphs,” International Journal of Recent Scientific Research, vol. 10, no. 6, pp. 33076-33081, 2019.
[Google Scholar] [Publisher Link]
[2] R. Bodendick, and G. Walther, “On Number Theoretical Methods in Graph Labelings,” Res Exp Maths vol. 2, pp. 3-25, 1995.
[Google Scholar]
[3] G. S. Bloom, and D. F. Hsu, “On Graceful Directed Graphs,” SIAM Journal on Algebraic Discrete Methods, vol. 6, no. 3, 1985.
[CrossRef] [Google Scholar] [Publisher Link]
[4] Joseph A. Gallian, “A Dynamic Survey of Graph Labelings,” Electronic Journal of Combinatorics, vol. 1, 2018.
[Google Scholar] [Publisher Link]
[5] Felix, E. Litta, and L. Benedict Michael Raj, “Changing and Unchanging Properties of Single Chromatic Transversal Domination Number of Graphs,” International Journal of Mathematics Trends and Technology, vol. 52, no. 4, pp. 262-266, 2017.
[CrossRef] [Google Scholar] [Publisher Link]
[6] F. Harary, Graph Theory, New Delhi: Narosa Publishing House, 2001.
[Google Scholar] [Publisher Link]
[7] S.M. Hegde, “Labeled Graphs and Digraphs: Theory and Application,” Research Promotion Workshop on IGGA, 2012.
[Google Scholar] [Publisher Link]
[8] E. Litta, and S. Maragatha Dharshini, “Proper Colourings in r - Regular Modified Zagreb Index Graph,” International Journal for Research in Applied Science and Engineering Technology, vol. 11, no. 3, pp. 1553-1558, 2023.
[CrossRef] [Google Scholar] [Publisher Link]
[9] E. Litta, and S. Datchini, “Proper Colourings in r – Regular Zagreb Index Graph,” Aryabhatta Journal of Mathematics and Informatics, vol. 15, no. 1, pp. 149-154, 2023.
[CrossRef] [Google Scholar] [Publisher Link]
[10] S. Saridha, and T. Rajaretnam “A Study On Plus Weighted Multiset Transformation Semigroups,” International Journal of Information and Computing Science, vol. 6, no. 1, pp. 84-98, 2019.
[Google Scholar] [Publisher Link]
[11] S. Saridha, and T. Rajaretnam, “Some Properties of Plus Weighted Finite State Automaton,” Journal of Computer and Mathematical Sciences, vol. 8, no. 11, pp. 674-690, 2017.
[Google Scholar] [Publisher Link]
[12] S. Saridha, and T. Rajaretnam “Some Properties of Plus Weighted Multiset Grammars,” International Journal of Information and Computing Science, vol. 6, no. 5, pp. 24-37, 2019.
[Google Scholar] [Publisher Link]
[13] S. Saridha, and S. Haridha Banu, “A New Direction Towards Plus Weighted Grammar,” International Journal for Research in Applied Science and Engineering Technology, vol. 11, no. 2, 2023.
[CrossRef] [Google Scholar] [Publisher Link]
[14] S. Saridha, and T. Jothika “An Introduction to Plus Weighted Dendrolanguage and its Properties,” Aryabhatta Journal of Mathematics and Informatics, vol. 15, no. 1, pp. 93-100, 2023.
[CrossRef] [Google Scholar] [Publisher Link]
[15] P. Shalini, and D. Paul Dhayabaran, “Generalization of Skolem Even Graceful Digraphs for Various Graphs”, International Journal of Mathematical Archive, vol. 5, no.4, pp. 65-69, 2014.
[Publisher Link]
[16] P. Shalini, and D. Paul Dhayabaran, “Skolem Graceful Signed Graphs on Directed Graphs,” Asian Journal of Current Engineering and Maths, vol. 3, no. 3, pp. 33-34, 2014.
[Google Scholar] [Publisher Link]
[17] P. Shalini, and D. Paul Dhayabaran “Generalization of Skolem Odd Graceful Digraphs for Various Graphs”, International Journal of Scientific and Research Technology, vol. 3, pp. 1-3, 2015.
[18] P. Shalini, and D. Paul Dhayabaran, “An Absolute Differences of Cubic and Square Difference Labeling,” International Journal of Advanced Scientific and Technical Research, vol. 3, no. 5, pp. 1-8, 2015.
[Google Scholar] [Publisher Link]
[19] P. Shalini, and D. Paul Dhayabaran, “A Study on Root Mean Square Labelings in Graphs,” International Journal of Engineering Science and Innovative Technology, vol. 4, no. 3, pp. 305-309, 2015.
[Google Scholar] [Publisher Link]
[20] P. Shalini, R. Gowri, and D. Paul Dhayabaran, “An Absolute Differences of Cubic and Square Difference Labeling for Some Families of Graphs,” The International Journal of Analytical and Experimental Modal Analysis, vol. 11, no. 10, pp. 538-544, 2019.
[Google Scholar] [Publisher Link]
[21] P. Shalini, and S. A Meena, “Lehmer -4 Mean Labeling of Graphs,” International Journal for Research in Applied Science and Engineering Technology, vol. 10, no. 12, pp. 1348-1351, 2022.
[CrossRef] [Google Scholar] [Publisher Link]
[22] P. Shalini, and S. Tamizharasi “Power-3 Heronian Odd Mean Labeling of Graphs,” International Journal for Research in Applied Science and Engineering Technology, vol. 10, no. 12, pp. 1605-1608. 2022.
[CrossRef] [Google Scholar] [Publisher Link]
[23] P. Shalini, and S. Tamizharasi, “A Study on Power-3 Heronian Odd Mean Labeling for Some Path Related Graphs”, International Journal for Research in Applied Science and Engineering Technology, vol. 11, no. 4, pp. 1136-1139, 2023.
[CrossRef] [Google Scholar] [Publisher Link]
[24] P. Shalini, and D. Madhumitha, “Root Cube Even Mean Labeling of Graph,” Aryabhatta Journal of Mathematics and Informatics, vol. 15, no. 1, pp. 33-38, 2023.
[CrossRef] [Google Scholar] [Publisher Link]
[25] P. Shalini, and S. A Meena, “Lehmer-4 Mean Labeling for Some Path Related Graphs,” Aryabhatta Journal of Mathematics and Informatics, vol. 15, no. 1, pp. 105-110, 2023.
[CrossRef] [Google Scholar] [Publisher Link]
[26] P. Shalini, “Skolem Odd Vertex Graceful Signed Graphs for Path,” Aryabhatta Journal of Mathematics and Informatics, vol. 15, no. 1, pp. 121-126, 2023.
[CrossRef] [Google Scholar] [Publisher Link]

Citation :

P. Shalini, "Skolem Odd Vertex Graceful Signed Graphs for Star Graph," International Journal of Mathematics Trends and Technology (IJMTT), vol. 69, no. 8, pp. 30-35, 2023. Crossref, https://doi.org/10.14445/22315373/IJMTT-V69I8P504