# EDGE IRREGULAR REFLEXIVE LABELING ON MONGOLIAN TENT GRAPH (M_(m,3)) AND DOUBLE QUADRILATERAL SNAKE GRAPH

• Diari Indriati Department of Mathematics, Faculty of Mathematics and Natural Sciences, Sebelas Maret University, Indonesia
• Tsabita Azzahra Department of Mathematics, Faculty of Mathematics and Natural Sciences, Sebelas Maret University, Indonesia
Keywords: Reflexive edge strength, Mongolian Tent Graph, Double Quadrilateral Snake Graph

### Abstract

Let G be an undirected, connected, and simple graph with edges set E(G)and vertex set V(G). An edge irregular reflexive k-labeling f is one in which the label for each edge is an integer number {1,2,…, k_e} and the label for each vertex is an even integer number {0,2,4,…,2k_v}, k = max{ k_e,2k_v}. This type of labeling results in distinct weights for each edge. The weight of an edge xy in a graph G with labeling f, indicated by wt (xy), is the total of the labels on the vertex that are incident to the edge as well as the edge label. The minimum value k of the largest label in the graph G is referred to as res (G), which stands for the reflexive edge strength of the graph G. The topic of edge irregular reflexive k-labeling for mongolian tent graph (M_(m,n)) and double quadrilateral snake graph (D(Q_n )) will be discussed in this paper. The res (M_(m,n)),m≥2,n=3 has been obtained that is ⌈(5m-1)/3⌉ for 5m-1≢2,3 (mod 6) and ⌈(5m-1)/3⌉+1 for 5m-1≡2,3 (mod 6). Also the res (D(Q_n )),n≥2 has been obtained that is ⌈(7n-7)/3⌉ for 7n-7≢2,3 (mod 6) and ⌈(5m-1)/3⌉+1 for 7n-7≡2,3 (mod 6).

### References

A. M. Marr and W. D. Wallis, Magic Graphs. Springer New York, 2012.

J. A. Gallian, “A dynamic survey of graph labeling,” Electron. J. Comb., vol. 1, no. DynamicSurveys, 2018.

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, pp. 1–11, 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.

J. A. Novelia and D. Indriati, “Edge irregular reflexive labeling on banana tree graphs B 2, nand B 3, n,” AIP Conf. Proc., vol. 2326, no. February, 2021, doi: 10.1063/5.0039316.

M. J. A. Khan, M. Ibrahim, and A. Ahmad, “On Edge Irregular Reflexive Labeling of Categorical Product of Two Paths,” Comput. Syst. Sci. Eng., vol. 36, no. 3, pp. 485–492, 2021, doi: 10.32604/csse.2021.014810.

J. L. G. Guirao, S. Ahmad, M. K. Siddiqui, and M. Ibrahim, “Edge irregular reflexive labeling for disjoint union of Generalized petersen graph,” Mathematics, vol. 6, no. 12, pp. 1–10, 2018, doi: 10.3390/math6120304.

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.

M. Ibrahim, M. J. A. Khan, and M. K. Siddiqui, “Edge irregular reflexive labeling for corona product of graphs,” Ars Comb., vol. 152, no. 3, pp. 263–282, 2020.

I. Hesti Agustin, I. Utoyo, Daflk, and M. D. Venkatachalam, “Edge irregular reflexive labeling of some tree graphs,” J. Phys. Conf. Ser., vol. 1543, no. 1, 2020, doi: 10.1088/1742-6596/1543/1/012008.

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. 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.

Arul, S. Mary, K. Subashini, “Cordial Labeling of Mongolian Tent M_n,” International Journal of Pure and Applied Mathematics, vol. 106, no. 8, p. 1-6, 2016.

N. I. S. Budi, “Kekuatan Sisi Refleksif pada Graf Tadpole, Graf Diamond Snake, Graf Quadrilateral Snake dan Graf K_1 ʘ_n P_3,”Skripsi, Prodi Matematika FMIPA UNS, 2021.

S. Anusha and A. Vijayalekshmi, “Dominator and total dominator chromatic number of Mongolian tent and fire cracker graphs,” Malaya J. Mat., vol. 8, no. 2, pp. 629–632, 2020, doi: 10.26637/mjm0802/0052.

A. Manonmani and R. Savithiri, “Double quadrilateral snakes on k-odd sequential harmonious labeling of graphs,” Malaya Journal of Matematik, vol. 3, no. 4, pp. 607–611, 2015.

Published
2023-12-18
How to Cite
[1]
D. Indriati and T. Azzahra, “EDGE IRREGULAR REFLEXIVE LABELING ON MONGOLIAN TENT GRAPH (M_(m,3)) AND DOUBLE QUADRILATERAL SNAKE GRAPH”, BAREKENG: J. Math. & App., vol. 17, no. 4, pp. 1933-1940, Dec. 2023.
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Articles