On edge irregularity strength of cycle-star graphs
DOI:
https://doi.org/10.22199/issn.0717-6279-5801Keywords:
Irregular assignment, irregularity strength, rregular total klabeling, edge irregularity strength, cycle-star graphAbstract
For a simple graph G, a vertex labeling ϕ : V (G) → {1, 2, . . . , k} is called k-labeling. The weight of an edge uv in G, written wϕ(uv), is the sum of the labels of end vertices u and v, i.e., wϕ(uv) = ϕ(u) + ϕ(v). A vertex k-labeling is defined to be an edge irregular k-labeling of the graph G if for every two distinct edges u and v, wϕ(u) ̸= wϕ(v). The minimum k for which the graph G has an edge irregular k-labeling is called the edge irregularity strength of G, written es(G). In this paper, we study the edge irregular k-labeling for cycle-star graph CSk,n−k and determine the exact value for cycle-star graph for 3 ≤ k ≤ 7 and n − k ≥ 1. Finally, we make a conjecture for the edge irregularity strength of CSk,n−k for k ≥ 8 and n − k ≥ 1.
References
Ahmad, A., Baca, M., Bashir, Y., & Siddiqui, M.K. (2012). Total edge irregularity strength of strong product of two paths. Ars Comb, 106, 449-459.
Ahmad, A., Baca, M., & Siddiqui, M.K. (2014). On edge irregular total labeling of categorical product of two cycles. Theory Comput. Syst, 54, 1-12.
Ahmad, A., Al-Mushayt, O., & Baca, M. (2014). On edge irregularity strength of graphs. Appl. Math. Comput, 243, 607-610.
Ahmad, A., Siddiqui, M.K., & Afzal, D. (2012). On the total edge irregularity strength of zigzag graphs. Australas. J. Comb, 54, 141-149.
Ahmad, A., Baca, M., & Nadeem, M.F. (2016). On the edge irregularity strength of Toeplitz graphs. U.P.B. Sci. Bull, 78, 155-162.
Ahmad, A., Al-Mushayt, O., & Siddiqui, M.K. (2012). On the total edge irregularity strength of hexagonal grid graphs. Australas. J. Comb, 53, 263-271.
Baca, M., Jendrol, S., Miller, M., & Ryan, J. (2007). On irregular total labellings. Discrete Math, 307, 1378-1388.
Baca, M., & Siddiqui, M.K. (2014). Total edge irregularity strength of generalized prism. Appl. Math. Comput, 235, 168-173.
Chartrand, G., Jacobson, M.S., Lehel, J., Oellermann, O.R., & Saba, F. (1988). Irregular networks. Congr. Numer, 64, 187-192.
Frieze, A., Gould, R.J., Karonski, M., & Finder, F. (2002). On graph irregularity strength. J. Graph Theory, 41, 120-137.
Gallian, J.A. (2019). A dynamic survey graph labeling. Electron. J. Comb, 19, 1-553.
Sedlar, J. (2013). Extremal unicyclic graphs with respect to additively weighted Harary index. Miskolic mathematical Notes, 16(2), 1-16.
Tarawneh, I., Hasni, R., & Ahmad, A. (2016). On the edge irregularity strength of corona product of graphs with paths. Appl. Math. E-Notes, 16, 80-87.
Tarawneh, I., Hasni, R., & Ahmad, A. (2016). On the edge irregularity strength of corona product of cycle with isolated vertices. AKCE Int. J. Graphs Comb, 13, 213-217.
Tarawneh, I., Hasni, R., Ahmad, A., & Lau, G.C. (2020). On the edge irregularity strength of corona product of graphs with cycle. Discrete Mathematics, Algorithms and Applications.
Tarawneh, I., Hasni, R., & Asim, M.A. (2018). On the edge irregularity strength of disjoint union of star graph and subdivision of star graph. Ars Comb, 141, 93-100.
Tarawneh, I., Hasni, R., Asim, M.A., & Siddiqui, M.A. (2019). On the edge irregularity strength of disjoint union of graphs. Ars Comb, 142, 239-249.
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