PL EN


Preferences help
enabled [disable] Abstract
Number of results
2021 | 156 | 40-61
Article title

Higher order triangular graceful labeling of some graphs

Content
Title variants
Languages of publication
EN
Abstracts
EN
A (p, q) graph G is said to admit higher order triangular graceful labeling if its vertices can be labeled by the integers from 0 to qth higher order triangular numbers such that the induced edge labels obtained by the absolute difference of the labels of end vertices are the first q higher order triangular numbers. A graph G which admits higher order triangular graceful labeling is called a higher order triangular graceful graph. In this paper, third order, fourth order, fifth order triangular graceful labeling are introduced and third order, fourth order, fifth order triangular graceful labeling of star graph, subdivision of star, nK_2, path, comb, bistar, coconut tree, nK_1,3 are studied.
Year
Volume
156
Pages
40-61
Physical description
Contributors
  • Department of Mathematics, The Madurai Diraviyam Thayumanavar Hindu College, Tirunelveli, Tamil Nadu, India
  • Department of Mathematics, The Madurai Diraviyam Thayumanavar Hindu College, Tirunelveli, Tamil Nadu, India
References
  • [1] F. Harary, Graph Theory, Adision - Wesley, Reading Mass, 1969.
  • [2] K. R. Parthasarathy, Basic Graph Theory, Tata Mcgraw Hill Publishing Company Limited, 1994
  • [3] M. Apostal, Introduction to Analytic Number Theory, Narosa Publishing House, Second Edition, 1991.
  • [4] David M. Burton, Elementary Number Theory, Second Edition, Wm. C. Brown Company Publishers, 1980.
  • [5] I. Niven and Herbert S. Zuckerman, An Introduction to the Theory of Numbers, Wiley Eastern Limited, Third Edition, 1991
  • [6] A. Rosa, On Certain Valuations of the Vertices of a Graph, Theory of Graphs (Proc. International Symposium, Rome, 1966), Gordon and Breach, N. Y and Dunad Paris (1967), 349-355
  • [7] S. W. Golomb, How to Number a Graph, Graph Theory and Computing, R. C. Read, Academic Press, New York (1972), 23-37
  • [8] B. D. Acharya, Construction of Certain Infinite Families of Graceful Graphs from a given graceful graph. Def. Sci. J. 32(3), (1982), 231-236
  • [9] S. Mahendran and K. Murugan, Pentagonal Graceful Labeling of Some Graphs. World Scientific News 155 (2021) 98-112
  • [10] R. Sakthi Sankari and M. P. Syed Ali Nisaya, Seond Order Triangular Gracful Graphs. World Scientific News 155 (2021) 140-154
  • [11] N. Meena, M. Madhan Vignesh. Strong Efficient Co-Bondage Number of Some Graphs. World Scientific News 145 (2020) 234-244
  • [12] J. A. Gallian, A Dynamic survey of Graph labeling, The Electronic Journal of Combinatorics, 22 (2019), #DS6
  • [13] M. Basker, P. Namasivayam, M. P. Syed Ali Nisaya. Some Results on Centered Triangular Sum Graphs. World Scientific News 155 (2021) 113-128
  • [14] K. Murugan, Square graceful labeling of Some Graphs. International Journal of Innovative Research in Science, Engineering and Technology 4(2) (2015) 511-520
  • [15] S. Murugesan, D. Jayaraman, J. Shiama, Some Higher Order Triangular Sum Labeling of Graphs. International Journal of Computer Applications, 72(10) (2013) 1-8
  • [16] D. S. T. Ramesh and M. P. Syed Ali Nisaya. Some Important Results on Pentagonal Graceful Graphs. International Journal of Applied Mathematical Sciences, 7(1) (2014) 71-77
  • [17] D. S. T. Ramesh and M. P. Syed Ali Nisaya. Some More Polygonal Graceful Labeling of Path. International Journal of Imaging Science and Engineering, 6(1) (2014) 901-905
  • [18] R. Sivaraman, Graceful Graphs and its Applications. International Journal of Current Research, 8(11), (2016), 41062-41067
  • [19] M. P. Syed Ali Nisaya and D. S. T. Ramesh, Pentagonal graceful labeling of Caterpillar Graphs. International Journal of Engineering Devlopment and Research 6(4) (2018) 150-154
  • [20] G. Muppidathi Sundari, K. Murugan. Extra Skolem Difference Mean Labeling of Some Graphs. World Scientific News 145 (2020) 210-221
  • [21] G. Muthumanickavel, K. Murugan. Oblong Sum Labeling of Union of Some Graphs. World Scientific News 145 (2020) 85-94
  • [22] Somasundaram and Ponraj, Mean labeling of Graphs. National Academy Science Letters (26) (2003) 210-213
  • [23] K. Thajeswari, S. Kirupa, Application of Graceful Graph in MPLS. International Journal for Scientific Research and Development, Vol. 6, Issue 06, (2018) 196-198
  • [24] Vasuki, A. Nagarajan and S. Arockiaraj, Even Vertex Odd Mean Labeling of Graphs. Sut J. Math 49(2) (2013) 79-92
  • [25] Frank Werner. Graph Theoretic Problems and their New Applications. Mathematics, S 445 (2020) 1-4
  • [26] M. Prema and K. Murugan, Oblong sum labeling of some graphs. World Scientific News 98 (2018) 12-22
  • [27] M. Vanu Esakki and M. P. Syed Ali Nisaya. Two Modulo Three Sum Graphs. World Scientific News 145 (2020) 274-285
  • [28] Venkatesh Srinivasan, Natarajan Chidambaram, Narasimhan Devadoss, Rajadurai Pakkirisamy & Parameswari Krishnamoorthi (2020) On the gracefulness of m-super subdivision of graphs, Journal of Discrete Mathematical Sciences and Cryptography, 23:6, 1359-1368, DOI: 10.1080/09720529.2020.1830561
  • [29] H. Yang, M.A. Rashid, S. Ahmad, M.K. Siddiqui, M. F. Hanif. Cycle super magic labeling of pumpkin, octagonal and hexagonal graphs. Journal of Discrete Mathematical Sciences and Cryptography 22(7), 1165-1176, (2019). DOI: 10.1080/09720529.2019.1698800
  • [30] L. Yan, Y. Li, X. Zhang, M. Saqlain, S. Zafar, M.R. Farahani. 3-total edge product cordial labeling of some new classes of graphs. Journal of Information & Optimization Sciences, 39(3) 2018, 705–724. DOI:10.1080/02522667.2017.1417727
  • [31] X. Zhang, F.A.Shah, Y. Li, L.Yan, A.Q. Baig, M.R. Farahani. A family of fifth-order convergent methods for solving nonlinear equations using variational iteration technique. Journal of Information and Optimization Sciences, 39(3), 2018, 673–694. DOI:10.1080/02522667.2018.1443628
  • [32] Xiaojing Yang, Junfeng Du, Liming Xiong. Forbidden subgraphs for supereulerian and Hamiltoniangraphs. Discrete Applied Mathematics Volume 288, 15 January 2021, Pages 192-200. https://doi.org/10.1016/j.dam.2020.08.034
  • [33] Kostochka, Alexandr, Yager, Derrek, Yu, Gexin 2020. Disjoint Chorded Cycles in Graphs with High Ore-Degree. Discrete Mathematics and Applications Vol. 165, p. 259. https://doi.org/10.1007/978-3-030-55857-4_11
  • [34] Costalonga, J.P., Kingan, Robert J., Kingan, Sandra R. 2021. Constructing Minimally 3-Connected Graphs. Algorithms, Vol. 14, Issue. 1, p. 9. https://doi.org/10.3390/a14010009
  • [35] Sullivan K, Rutherford D, Ulness DJ. Centered Polygonal Lacunary Graphs: A Graph Theoretic Approach to p-Sequences of Centered Polygonal Lacunary Functions. Mathematics 2019; 7(11): 1021. https://doi.org/10.3390/math7111021
  • [36] M. Vanu Esakki, M. P. Syed Ali Nisaya, Some Results on Two Modulo Three Sum Graphs. Journal of Xidian University, 14(9) (2020) 1090-1099
  • [37] Chiba, Shuya, Yamashita, Tomoki, 2018. Degree Conditions for the Existence of Vertex-Disjoint Cycles and Paths: A Survey. Graphs and Combinatorics, Vol. 34, Issue. 1, p. 1. https://doi.org/10.1007/s00373-017-1873-5
  • [38] Molla, Theodore; Santana, Michael; Yeager, Elyse, 2020. Disjoint cycles and chorded cycles in a graph with given minimum degree. Discrete Mathematics, Vol. 343, Issue. 6, p. 111837. https://doi.org/10.1016/j.disc.2020.111837
Document Type
article
Publication order reference
Identifiers
YADDA identifier
bwmeta1.element.psjd-ed0e2587-e5d1-478f-86e7-f2dfac30fc53
JavaScript is turned off in your web browser. Turn it on to take full advantage of this site, then refresh the page.