THE REFLEXIVE EDGE STRENGTH OF THE PENTAGONAL SNAKE GRAPH AND CORONA OF THE OPEN TRIANGULAR LADDER AND NULL GRAPH
Abstract
Assume that be an undirected simple graph with vertex set and edge set . The edge irregular reflexive -labeling of graph is a labeling selects positive integers from 1 to as edge labels and non negative even numbers from 0 to as vertex labels, and the weights assigned to each edge are distinct, where . On graph with labeling, the weight of edge is represented by which is defined as the sum of edge label and all vertex labels incident to that edge. Reflexive edge strength of graph is the minimum of the highest label, denoted by . In this research, reflexive edge strength for pentagonal snake graph and corona of open triangular ladder and null graph will be determined. The method of this research is literature study, the lower bound of determined by Ryan’s lemma and the upper bound by labeling. The reflexive edge strength of pentagonal snake graph with is for and for The reflexive edge strength of corona of open triangular ladder and null graph with n ≥ 3 and m ≥ 1 is and .
Downloads
References
W. D. Wallis, "Magic Graphs", Springer Science & Business Media, 2012.
J. A. Gallian, " A Dynamic Survey of Graph Labeling", The Electronic Journal of Combinatories, 2023.
M. Bača, S. Jendrol’, M. Miller, and J. Ryan, “On irregular total labellings,” Discrete Math., vol. 307, no. 11–12, pp. 1378–1388, 2007, doi: 10.1016/j.disc.2005.11.075.
M. Bača, M. Irfan, J. Ryan, A. Semaničová-Feňovčíková, and D. Tanna, “On edge irregular reflexive labellings for the generalized friendship graphs,” Mathematics, vol. 5, no. 4, 2017, doi: 10.3390/math5040067.
D. Tanna, J. Ryan, and A. Semaničová-Feňovčíková, “Edge irregular reflexive labeling of prisms and wheels,” Australas. J. Comb., vol. 69, no. 3, pp. 394–401, 2017.
R. Junetty, D. Indriati, and B. Winarno, “Edge Irregular Reflexive Labeling of Palm Tree Graph
C3−B2,r and C3−B3,r,” AIP Conf. Proc., vol. 2566, no. 1, 2022, doi: 10.1063/5.0116566.
D. Indriati and T. Azzahra, “Edge Irregular Reflexive Labeling on Mongolian Tent Graph (M_(m,3)) and Double Quadrilateral Snake Graph,” BAREKENG J. Ilmu Mat. dan Terap., vol. 17, no. 4, pp. 1933–1940, 2023, doi: 10.30598/barekengvol17iss4pp1933-1940.
K. K. Yoong, R. Hasni, G. C. Lau, M. A. Asim, and A. Ahmad, “Reflexive edge strength of convex polytopes and corona product of cycle with path,” AIMS Math., vol. 7, no. 7, pp. 11784–11800, 2022, doi: 10.3934/math.2022657.
D. Indriati, Widodo, and I. Rosyida, “Edge Irregular Reflexive Labeling on Corona of Path and Other Graphs,” J. Phys. Conf. Ser., vol. 1489, no. 1, 2020, doi: 10.1088/1742-6596/1489/1/012004.
I. H. Agustin, Dafik, M. Imam Utoyo, Slamin, and M. Venkatachalam, “The reflexive edge strength on some almost regular graphs,” Heliyon, vol. 7, no. 5, p. e06991, 2021, doi: 10.1016/j.heliyon.2021.e06991.
I. Setiawan and D. Indriati, “Edge Irregular Reflexive Labeling on Sun Graph and Corona of Cycle and Null Graph with Two Vertices,” Indones. J. Comb., vol. 5, no. 1, p. 35, 2021, doi: 10.19184/ijc.2021.5.1.5.
W. I. Saputri and D. Indriati, “Kekuatan sisi refleksif pada graf rantai segitiga ,” SeNa-MaGeStiK., pp. 418–425, July. 16, 2022.
L. A. Zalzabila, D. Indriati, and T. S. Martini, “Edge Irregular Reflexive Labeling on Alternate Triangular Snake and Double Alternate Quadrilateral Snake,” BAREKENG J. Ilmu Mat. dan Terap., vol. 17, no. 4, pp. 1941–1948, 2023, doi: 10.30598/barekengvol17iss4pp1941-1948.
S. Nurhayati and Y. Susanti, “An Edge Irregular Reflexive k−labeling of Comb Graphs with Additional 2 Pendants,” J. Mat. Integr., vol. 19, no. 1, p. 91, 2023, doi: 10.24198/jmi.v19.n1.41624.89-108.
V. Rievaldo Wijaya and L. Damayanti Ningrum, “Edge Irregular Reflexive Labeling on Lobster Graph,” J. Math. Sci. Optim., vol. 1, no. 1, pp. 37–43, 2024, doi: 10.31258/jomso.1.1.37-43.
S. Dhanalakshmi and S. Thirunavukkarasu, “Mean Square Cordial Labeling Of Some Pentagonal Snake Graphs,” I3CAC 2021, June. 7-8, 2022. doi: 10.4108/eai.7-6-2021.2308859.
P. Sumathi, A. Rathi, and A. Mahalakshmi, “Quotient Labeling of Corona of Ladder Graphs,” vol. 1, no. 3, pp. 80–85, 2017, doi: 10.29027/IJIRASE.v1.i3.2017.80-85.
Copyright (c) 2024 Diari Indriati, Risma Listya Utami, Putranto Hadi Utomo
This work is licensed under a Creative Commons Attribution-ShareAlike 4.0 International License.
Authors who publish with this Journal agree to the following terms:
- Author retain copyright and grant the journal right of first publication with the work simultaneously licensed under a creative commons attribution license that allow others to share the work within an acknowledgement of the work’s authorship and initial publication of this journal.
- Authors are able to enter into separate, additional contractual arrangement for the non-exclusive distribution of the journal’s published version of the work (e.g. acknowledgement of its initial publication in this journal).
- Authors are permitted and encouraged to post their work online (e.g. in institutional repositories or on their websites) prior to and during the submission process, as it can lead to productive exchanges, as well as earlier and greater citation of published works.
1.gif)
