Total Edge Irregularity Strength of Some Graphs
DOI:
https://doi.org/10.64137/31082637/IJMAR-V1I2P103Keywords:
Irregularity Strength, Total Edge Irregularity Strength, Edge Irregular Total LabelingAbstract
An edge irregular total k-labeling of a graph G = (V,E) is a labeling of vertices and edges of G in such a way that for any two different edges uv and u1v1 their weight and are distinct. The total edge irregularity strength, tes(G), is defined as the minimum k for which the graph G has an edge irregular total k-labeling. In this paper, we study the total edge irregularity strength of joint-Wheel graph WHn, < Wn : Wm > and path union of graph.
References
[1] Ahmad and M. Baˇ ca, Egde irregular total labeling of certain family of graphs, AKCE. J. Graphs., Combin., 6 (1), (2009), 21-29.
[2] Ahmad and M. Baˇ ca, Y. Bashir and M. K. Siddiqui, Total egde irregularity strength of strong product of two paths, Ars Combin., 106, (2012), 449-459.
[3] M. Baˇ ca, S. Jendroˇ l, M. Miller and J. Ryan, On irregular total labellings, Discrete Math., 307, (2007), 1378-1388.
[4] T.Bohman and D.Kravitz, On the irregularity strength of trees, J. Graph Theory, 45, (2004), 241-254
[5] Florian Pfender, Total edge irregularity strength of large graphs, Discrete Math., 312, (2009), 229-237.
[6] Ivanˇ co and S.Jendroˇ l, Total irregularity strength of trees, Discussiones Math. Graph Theory, 26, (2006), 449-456.
[7] P.Jeyanthi and A.Sudha, Total edge irregularity strength of wheel related graphs, Journal of Graph Labeling, 2(1) (2015), 45-57.
[8] P.Jeyanthi and A.Sudha, Total Edge Irregularity Strength of Disjoint Union of Wheel Graphs, Electron. Notes in Discrete Mathematics, 48 (2015), 175-182
[9] P. Jeyanthi and A.Sudha, Total Edge Irregularity Strength of Disjoint Union of Dou ble Wheel Graphs, Proyecciones Journal of Mathematics, Vol. 35, No.3 (2016), 251-262
[10] P. Jeyanthi and A.Sudha, Total edge irregularity strength of some families of graphs, Utilitas Mathematica,vol.109,(2018) 139-153.
[11] P. Jeyanthi and A.Sudha, Some results on edge irregular total labeling, Journal of the International Mathematical Virtual Institute, vol.9 (2019)73-91
[12] P. Jeyanthi and A.Sudha, On the total irregularity strength of wheel related graphs, Utilitas Mathematica, vol.110 (2019)131-144.
[13] Stanislav Jendroˇ l, Jozef Miˇ skuf, Roman Sot´ ak, Total edge irregularity strength of complete graphs and complete bipartite graphs, Discrete Math., 310, (2010), 400 407.
[14] Stephan Brandt, Jozef Miˇ skuf and Dieter Rautenbach, Edge irregular total labellings for graphs of linear size, Discrete Math., 309, (2009), 3786-3792
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