Preferences help
enabled [disable] Abstract
Number of results
2021 | 156 | 1-12
Article title

Some Results on Octagonal Graceful Graphs

Title variants
Languages of publication
Numbers of the form On = n (3n-2) for all n≥1 are called octagonal numbers. Let G be a graph with p vertices and q edges. Let f: V (G) → {0, 1, 2… Om} where Om is the mth octagonal number be an injective function. Define the function f*:E(G) → {1,8,21,..,Om} such that f*(uv) = |f(u)-f(v)| for all edges uvϵE(G). If f*(E (G)) is a sequence of distinct consecutive octagonal numbers {O1, O2 , …, Oq }, then the function f is said to be octagonal graceful labeling and the graph which admits such a labeling is called a octagonal graceful graph. In this paper, octagonal graceful labeling of some graphs is studied.
Physical description
  • 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
  • [1] B. D. Acharya, Construction of Certain Infinite Families of Graceful Graphs from a given graceful graph. Def. Sci. J. 32(3) (1982) 231-236
  • [2] M. Apostal, Introduction to Analytic Number Theory, Narosa Publishing House, Second Edition, 1991.
  • [3] J. C. Berbond, Graceful Graphs, Radio Antennae and French Wind Mills, Graph Theory and Combinatories, Pitman, London, (1979), 13-17
  • [4] J. A. Bondy and U. S. R. Murty, Graph Theory with Applications, Macmillan Press, London, 1976.
  • [5] J. Devaraj (2002), A Study on Different Classes of Graphs and their Labelings, Ph.D. Thesis, University of Kerla, India
  • [6] J. A. Gallian. A Dynamic survey of Graph labeling. The Electronic Journal of Combinatorics, 22 (2019), #DS6
  • [7] F. Harary, Graph Theory, Adision - Wesley, Reading Mass, 1969.
  • [8] S. W. Golomb, How to Number a Graph, Graph Theory and Computing, R. C. Read, Academic Press, New York (1972), 23-37
  • [9] S. Mahendran and K. Murugan, Pentagonal Graceful Labeling of Some Graphs. World Scientific News 155 (2021) 98-112
  • [10] K. Murugan, Square graceful labeling of Some Graphs. International Journal of Innovative Research in Science, Engineering and Technology, 4(2) (2015) 511-520
  • [11] K. Murugan and A. Subramanian, Skolem Difference Mean Graphs. Mapana J Sci 11, 4, (2012) 109-120
  • [12] S. Murugesan, D. Jayaraman, J. Shiama, Some Higher Order Triangular Sum Labeling of Graphs. International Journal of Computer Applications, 72(10) (2013) 1-8
  • [13] G. Muthumanickavel, K. Murugan, Oblong Sum Labeling of Union of Some Graphs. World Scientific News 145 (2020) 85-94
  • [14] I. Niven and Herbert S. Zuckerman, An Introduction to the Theory of Numbers, Wiley Eastern Limited, Third Edition, 1991
  • [15] K. R. Parthasarathy, Basic Graph Theory, Tata Mcgraw Hill Publishing Company Limited, 1994
  • [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] A. Rosa, On Certain Valuations of the Vertices of a Graph, Theory of Graphs (Proc. Internat. Symposium, Rome, 1966), Gordon and Breach, N. Y and Dunad Paris (1967), 349-355
  • [19] R. Sakthi Sankari and M. P. Syed Ali Nisaya, Seond Order Triangular Gracful Graphs. World Scientific News, 155 (2021) 140-154
  • [20] R. Sivaraman, Graceful Graphs and its Applications. International Journal of Current Research, 8(11), (2016) 41062-41067
  • [21] 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
  • [22] T. Tharmaraj and P. B. Sarasija, Square graceful graphs, International Journal of Mathematics and soft Computing, Vol. 4, No.1, (2014) 129-137
  • [23] T. Tharmaraj and P. B. Sarasija, Some Square graceful Graphs, International Journal of Mathematics and Soft Computing, Vol. 5, No.1, (2015) 119-127
  • [24] M. Vanu Esakki, M. P. Syed Ali Nisaya. Two Modulo Three Sum Graphs. World Scientific News 145 (2020) 274-285
  • [25] M. Basker, P. Namasivayam, M. P. Syed Ali Nisaya. Some Results on Centered Triangular Sum Graphs. World Scientific News 155 (2021) 113-128
  • [26] 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
  • [27] N.Vedavathi, Dharmaiya Gurram, Applications on Graph Theory. International Journal of Engineering Research and Technology, Vol. 2, Issue 1, (2013) 1-4
  • [28] G. Muppidathi Sundari & K. Murugan, Extra Skolem Difference Mean Labeling of Some Graphs. World Scientific News 145 (2020) 210-221
  • [29] N. Meena, M. Madhan Vignesh. Strong Efficient Co-Bondage Number of Some Graphs. World Scientific News 145 (2020) 234-244
  • [30] Frank Werner.Graph Theoretic Problems and their New Applications. Mathematics, S 445, (2020) 1-4
  • [31] Xiaojing Yang, Junfeng Du, Liming Xiong. Forbidden subgraphs for supereulerian and Hamiltoniangraphs. Discrete Applied Mathematics Volume 288, 15 January 2021, Pages 192-200.
  • [32] 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.
  • [33] 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.
  • [34] Kostochka, Alexandr, Yager, Derrek, Yu, Gexin 2020. Disjoint Chorded Cycles in Graphs with High Ore-Degree. Discrete Mathematics and Applications Vol. 165, p. 259.
  • [35] Costalonga, J.P., Kingan, Robert J., Kingan, Sandra R. 2021. Constructing Minimally 3-Connected Graphs. Algorithms, Vol. 14, Issue. 1, p. 9.
  • [36] 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
  • [37] 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
  • [38] 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
  • [39] 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
Document Type
Publication order reference
YADDA identifier
JavaScript is turned off in your web browser. Turn it on to take full advantage of this site, then refresh the page.