Vertex Antimagic Edge Slither Labeling of Nigh Complete Bipartite Graph
DOI:
https://doi.org/10.31305/rrijm.2026.v11.n04.003Keywords:
Nigh Complete Bipartite Graph, Antimagic Labeling, Slither LabelingAbstract
Graphs are simple structures that are easy to understand and fathom. Graphs can be classified into different types based on their structure one such type is the bipartite graph. A nigh complete bipartite graph or a nigh graph is an adaptation of a bipartite graph that is defined as Km, n + e1 + e2 such that the graph becomes a complete bipartite graph when the two edges e1 and e2 are removed. In this paper, the approval of vertex antimagic edge slither labeling to nigh complete bipartite graph is established.
References
[1] R. Bodendiek and G. Walther – Arithmetisch Antimagische Graphen, In K. Wagner and R. Bodendiek eds. Graphentheorie 111, BI – WISS, Mannheim, 1993
[2] R. Bodendiek and G. Walther – On number theoretical methods in Graph Lebelings – Res. Exp. Math. 21 (1995), 3 – 25
[3] R. Bodendiek and G. Walther –On arithmetic antimagic edge labeling of graphs, Mitt. Math. Ges. Hamburg 17 (1998), 85 – 89
[4] R.C. Bunge, S.I. El-Zanati, W.O’Hanlon and C. Vanden Eynden - On γ-Labeling the almost bipartite graph Pm + e - 4520 Mathematics Department, Illinois State University, Normal, Illinois 61790-4520, USA
[5] N. Hartsfield and G. Ringel – Pearls in Graph Theory, Academic Press, Boston – San Diego – New York – London, 1990
[6] Martin Baca and Mirka Miller – Super Edge Antimagic Graphs – A Wealth of Problems and Some Solutions – Brown Walker Press, June 2008 ISBN – 10: 1-59942-466-5 (e-book), ISBN – 13: 978-1-59942-466-8 (e-book)
[7] J.A. Macdougall, M. Miller, Slamin and W.D. Wallis – Vertex Magic Total Labeling of Graphs – Utilitas Math. 61 (2002), 3 – 21
[8] J.A. Macdougall, M. Miller and W.D. Wallis – Vertex Magic Total Labeling of Wheels and Related Graphs – Utilitas Math. 62 (2002), 175 – 183
[9] J. Sedlacek – Problem 27, In – Theory and its Applications, Proc. Symp. Smolenice, 1963, 163 – 169
[10] J. Sedlacek – On Magic Graphs – Math. Slovaca 26 (1976), 329 – 335.
[11] R. Sreenivasan and M.S. Paulraj – Vertex Antimagic Edge Labeling of Nigh Complete Bipartite Graph – International Journal of Research and Analytical Reviews, Vol 5, Issue 4, November 2018.
