EDGE IRREGULAR REFLEXIVE LABELING ON LOBSTER GRAPH
DOI:
https://doi.org/10.31258/jomso.1.1.37-43Keywords:
lobster graph, total labeling, irregular labeling, reflexive labeling, reflexive edge strengthAbstract
Let $G$ be a lobster graph that have three layer of vertices where each layer is connected to each other. The total labeling of the graph is called an edge irregular reflexive $k$-labeling if the total weight of two incident vertices and the edge that joins it is different for all possible edges on the graph. In this paper, we will further discuss the minimum number of $k$ for this kind of labeling on lobster graph. In particular, we determine the exact value of the reflexive edge strength of lobster graph. To help illustrate it, we use Python code to generate the label for the graph.
References
Ahmad, A., 2012, On the total edge irregularity strength of zigzag graphs, Australian Journal of Combinatorics, Volume : 54 pp 141-149.
Bacˇa et al., 2018, Note on edge irregular reflexive labelings of graphs, AKCE International Journal and Graphs and Combinatorics.
Bacˇa, M., and Siddiqui, M. K., 2014, Total edge irregularity strength of generalized prism, Applied Mathematics and Computation, Volume : 235 pp 168–173.
Chartrand, G., Jacobson, M.S., Lehel, J., Oellermann, O.R., Ruiz, S., and Saba, F., 1988, Irregular networks, Congr. Numer., Volume : 64 pp 187–192.
Agustin, H.I., Utoyo, I., Dafik, D., and Venkatachalam, M., 2020, Edge irregular reflexive labeling of some tree graphs, Journal of Physics: Conference Series, 1543 (1), 012008.
Indriati, D., Widodo, W., and Rosyida, I, 2020, Edge irregular reflexive labeling on corona of path and other graphs, Journal of Physics: Conference Series, 1489 (1), 012004.
Indriati et al, 2020, On the total edge irregularity strength of generalized helm, AKCE International Journal and Graphs and Combinatorics.
Tanna, D., Ryan J., and Fenovcikova, A.S., 2017, Edge irregular reflexive labeling of prisms and wheels, Australian Journal of Combinatorics, Volume : 69 (3) pp 394-401.
Zhang, X., Ibrahim, M., Bokhary, S., and Siddiqui, M., 2018, Edge Irregular Reflexive Labeling for the Disjoint Union of Gear Graphs and Prism Graphs, Mathematics, Volume : 6 (9) pp 142.
Downloads
Published
Versions
- 2024-03-13 (2)
- 2023-07-31 (1)
