TARU PUBLICATIONS
Journal of Discrete Mathematical Sciences and Cryptography cover
Open Access ·Peer-reviewed·ISSN (Online): 2169-0065·ISSN (Print): 0972-0529

Monthly Journal: Publishes theoretical and applied research in all areas of Discrete Mathematical Sciences, Cryptography, Combinatorics, Elliptic Curves and Information Security.

Issues up to 2022 co-published with and available at:Taylor & Francis Online
submissions@tarupublications.com
Open Access Research Article

On k-super graceful graphs with extremal maximum vertex degree

* , , , ,

* Corresponding author · click or hover a name for details

pp. 1765–1783Vol. 27Issue 6September 2024DOI: 10.47974/JDMSC-1722 Crossmark XML
Received:
08 Jun 2022
Accepted:
16 Nov 2022
Published Online:
16 Sep 2024
Article type:
Research Article
Language:
EN
Article no.:
JDMSC-1722
Pages:
1765–1783

Abstract

Let G(V, E) be a simple and loopless graph with |V|  vertices and |E|  edges. For k ≥ 1,  a graph G is called k-super graceful if there is a bijective labeling f : V ∪ E → {i | k ≤ i ≤ k + |V| + |E| – 1} with f(vu) = |f(v) – f(u)|  for every edge uv ∈ E.  In this paper, we study the existence of k-super graceful labeling of certain graphs with extremal maximum vertex degree.

Keywords

Subject Classifications

(2010) 05C78

References

[1] D.W. Bange, A.E. Barkauskas and P.J. Slater, Sequentially additive graphs, Discrete Math., 44, 235-241 (1983).
[2] M. Basher, Odd-even graceful labeling of planar grid and prism graphs, J. Inf. Optim. Sci., 42:4, 747-751 (2021). DOI: 10.1080/02522667.2020.1800787.
[3] J.A. Bondy, U.S.R. Murty, Graph theory with applications, New York, MacMillan (1976).
[4] R. Boonklurb, N. Ruamkaew and S. Singhun, Directed edge-graceful labeling of digraph consisting of c cycles of the same size, J. Discrete Math. Sci. Cryptogr., 25:1, 53-72 (2022). DOI: 10.1080/09720529.2021.1925448.
[5] J.A. Gallian, A dynamic survey of graph labeling, Electron. J. Combin., 23 #DS6 (2019).
[6] P. Hajnal, G. Nagy, Simply sequentially additive labelings of 2-regular graphs, Discrete Math., 310, 922-928 (2010).
[7] S.M. Hegde and M. Miller, Further results on sequentially additive graphs, Discuss. Math. Graph Theory, 27, 251-268 (2007).
[8] G.C. Lau, W.C. Shiu and H.K. Ng, Further results on super graceful labeling of graphs, AKCE Int. J. Graphs Comb., 13 (2), 200-209 (2016).
[9] G.C. Lau, W.C. Shiu and H.K. Ng, On k-super graceful labeling of graphs, Thai. J. Maths., 20(3), 1375-1387 (2022).
[10] K. Manimekalai, J. Baskar Babujee and K. Thirusangu, Simply sequentially additive labeling of some special trees, Appl. Math. Sci., Vol. 6 (131), 6501-6514 (2012).
[11] M.A. Perumal, S. Navaneethakrishnan, S. Arockiaraj and A. Nagarajan, Super graceful labeling for some special graphs, Int. J. Research and Reviews in Appl. Sci., 9 (3), 382-404 (2011).
[12] M.A. Perumal, S. Navaneethakrishnan, S. Arockiaraj and A. Nagarajan, Super graceful labeling for some simple graphs, Int. J. Math. and Soft Computing, Vol 2 (1), 35-49 (2012).
[13] A. Rosa, On certain valuations of the vertices of a graph, Theory of Graphs International Symposium, Rome (1966).
[14] Th. Skolem, On certain distributions of integers into pairs with given differences, Math. Scand. 5, 57-68 (1957).
[15] P.J. Slater, On k-sequential and other numbered graphs, Discrete Math., 34, 185-193 (1981). 

Views: 424Downloads: 118Citations: 0