Edge-Odd Graceful Labeling of Graph Obtained from A Vertex Deletion on A Comb Graph

Main Article Content

Siwaporn Saewan
Jitsupa Hnusiri


An edge-odd graceful labeling of a graph gif.latex?G with gif.latex?q edges is a bijection gif.latex?f from the set of edges of the graph to gif.latex?\{1,3,5,\ldots,2q-1\} such that each vertex is assigned the sum of labels of all edges incident to it modulo gif.latex?2q. The resulting vertex labels are distinct. A graph gif.latex?G is called an edge-odd graceful graph if it admits an edge-odd graceful labeling gif.latex?f. In this paper, we show that the new graphs obtained by deleting a pendant vertex of the comb graph are edge-odd graceful graphs.

Article Details

How to Cite
Saewan, S., & Hnusiri, J. (2021). Edge-Odd Graceful Labeling of Graph Obtained from A Vertex Deletion on A Comb Graph. Mathematical Journal by The Mathematical Association of Thailand Under The Patronage of His Majesty The King, 66(704), 46–62. Retrieved from https://ph02.tci-thaijo.org/index.php/MJMATh/article/view/241484
Research Article


ศิวพร แซ่วัน, ธนาภา ขาวมัน, วราภรณ์ แดงนภาพรกุล และสุมิตา แก้วทอง. (2563). การกำกับแบบเกรซฟูลในบริบทการทำซ้ำองค์ประกอบของกราฟ. วารสารมหาวิทยาลัยทักษิณ, 23 (1), หน้า 11 – 19.

Saewan, S., Khawman, T., Dangnapaponkul, W. and Kaewthong, S. (2020). Graceful Labeling in The Context of Duplication of Graph Element. Thaksin Journal, 23 (1), p. 11 – 19.

Boxwala, S. A. and Vashishta, P. (2015). Some New Families of Graceful Graphs. Electronic Notes in Discrete Mathematics, 48, p. 127 – 133.

Cattell, R. (2007). Graceful Labellings of Paths. Discrete Mathematics, 307 (24), p. 3161 – 3176.

Daoud, S. N. (2017). Edge-Odd Graceful Labeling of Some Path and Cycle Related Graph. AKCE International Journal of Graphs and Combinatorics, 14, p. 178 – 203.

Golomb, S. W. (1972). How to Number A Graph. In R. C. Read (Ed.). Graph Theory and Computing. p. 23 – 37. New York, U. S. A. Academic Press.

Kaneria, V. J., Makadia, H. M. and Jariya, M. M. (2014). Graceful Labeling for Cycle of Graph. International Journal of Mathematics Research, 6 (2), p. 173 – 178.

Koh, K. M., Phoon, L. Y. and Soh, K. W. (2015). The Gracefulness of The Join of Graphs (II). AKCE International Journal of Graphs and Combinatorics, 12 (2 – 3), p. 180 – 185.

Rosa, A. (1967). On Certain Valuations of The Vertices of A Graph. (In Theory of Graphs, International Symposium, Rome, July, 1966), New York: Gordon and Breach.

Seoud, M. and Salim, M. (2016). Further Results on Edge-Odd Graceful Graphs. Turkish Journal of Mathematics, 40, p. 647 – 656.

Singhun, S. (2013). Graphs with Edge-Odd Graceful Labelings. International Mathematical Forum, 8 (12), p. 577 – 582.

Solairaju, A., Balasubramanian, G. and Ambika, B. (2017). Edge-Odd Graceful Labeling for Sum of A Path and A Finite Path. Global Journal of Mathematical Science: Theory and Practical, 9 (3), p. 323 – 335.

Solairaju, A. and Chithra, K. (2009). Edge-Odd Graceful Graphs. Electronic Notes in Discrete Mathematics, 33, p. 15 – 20.

Tamilarasan, T., Rajeswari, V. and Thiagarajan. (2018). Edge-Odd Graceful Labeling of Some Special Graphs. International Journal of Mathematics Trends and Technology, 56 (2). p. 109 – 112

Tirasuwanwasee, A. (2015). Edge-Odd Graceful Labelings of Prism-Like Graphs of Cycles. (Master’s thesis). Chulalongkorn University. Faculty of Science. Retrieved from: http://cuir.car.chula.ac.th/handle/123456789/61639.