On total edge irregularity strength for some special types of uniform theta snake graphs

Fatma Salama; Randa M. Abo Elanin; Fatma Salama; Randa M. Abo Elanin

doi:10.3934/math.2021471

AIMS Mathematics

2021, Volume 6, Issue 8: 8127-8148. doi: 10.3934/math.2021471

Previous Article Next Article

Research article

On total edge irregularity strength for some special types of uniform theta snake graphs

Fatma Salama ^{1
,
,},
Randa M. Abo Elanin ^2,3

1.
Mathematics Department, Faculty of Science, Tanta University, Tanta, Egypt
2.
Mathematics Department, Faculty of Science, Taibah University, Al-Madinah Al-Munawwarah, Saudi Arabia
3.
Mathematics Department, Faculty of Science, Al-Azhar University (Girls Branchs), Nasr City, Cairo, Egypt

Received: 18 February 2021 Accepted: 16 May 2021 Published: 24 May 2021
MSC : 05C78, 05C38

A labeling of a connected, simple and undirected graph G(V, E) is a map that assigns the elements of a graph G with positive numbers. Many types of labeling for graph are found and one of them is a total edge irregularity strength (TEIS) of G, which denoted by tes(G). In the current paper, we defined a new type of family of graph called uniform theta snake graph, $\theta_{n}(t, m)$. Also, the exact values of total edge irregularity strengths for some special types of the new family have been determined.
- irregular labelling,
- total edge irregularity strength,
- edge irregular total labeling,
- uniform theta snake graph
Citation: Fatma Salama, Randa M. Abo Elanin. On total edge irregularity strength for some special types of uniform theta snake graphs[J]. AIMS Mathematics, 2021, 6(8): 8127-8148. doi: 10.3934/math.2021471

Related Papers:

Abstract

A labeling of a connected, simple and undirected graph G(V, E) is a map that assigns the elements of a graph G with positive numbers. Many types of labeling for graph are found and one of them is a total edge irregularity strength (TEIS) of G, which denoted by tes(G). In the current paper, we defined a new type of family of graph called uniform theta snake graph, $\theta_{n}(t, m)$. Also, the exact values of total edge irregularity strengths for some special types of the new family have been determined.

References

[1]	A. Ahmad, M. K. Siddiqui, D. Afzal, On the total edge irregularity strength of zigzag graphs, Australas. J. Comb., 54 (2012), 141-149.
[2]	A. Ahmad, M. Arshad, G. Ižaríková, Irregular labelings of helm and sun graphs, AKCE Int. J. Graphs Combinatorics, 12 (2015), 161-168. doi: 10.1016/j.akcej.2015.11.010
[3]	A. Ahmad, M. Bača, M. K. Siddiqui, On edge irregular total labeling of categorical product of two cycles, Theory Comput. Syst., 54 (2014), 1-12. doi: 10.1007/s00224-013-9470-3
[4]	A. Ahmad, M. Bača, Total edge irregularity strength of a categorical product of two paths, Ars Comb., 114 (2014), 203-212.
[5]	A. Ahmad, O. B. S. Al-Mushayt, M. Bača, On edge irregularity strength of graphs, Appl. Math. Comput., 243 (2014), 607-610.
[6]	A. Ahmad, M. K. Siddiqui, M. Ibrahim, M. Asif, On the total irregularity strength of generalized Petersen graph, Math. Rep., 18 (2016), 197-204.
[7]	A. Ahmad, M. Bača, Edge irregular total labeling of certain family of graphs, AKCE Int. J. Graphs. Combinatorics, 6 (2009), 21-29.
[8]	O. Al-Mushayt, A. Ahmad, M. K. Siddiqui, On the total edge irregularity strength of hexagonal grid graphs, Australas. J. Comb., 53 (2012), 263-271.
[9]	D. Amar, O. Togni, Irregularity strength of trees, Discrete Math., 190 (1998), 15-38. doi: 10.1016/S0012-365X(98)00112-5
[10]	M. Bača, S. Jendroî, M. Miller, J. Ryan, On irregular total labellings, Discrete Math., 307 (2007), 1378-1388. doi: 10.1016/j.disc.2005.11.075
[11]	M. Bača, M. K. Siddiqui, Total edge irregularity strength of generalized prism, Appl. Math. Comput., 235 (2014), 168-173.
[12]	S. Brandt, J. Miškuf, D. Rautenbach, On a conjecture about edge irregular total labellings, J. Graph Theory, 57 (2008), 333-343. doi: 10.1002/jgt.20287
[13]	N. Hinding, N. Suardi, H. Basir, Total edge irregularity strength of subdivision of star, J. Discrete Math. Sci. Cryptography, 18 (2015), 869-875. doi: 10.1080/09720529.2015.1032716
[14]	D. Indriati, Widodo, I. E. Wijayanti, K. A. Sugeng, M. Bača, On total edge irregularity strength of generalized web graphs and related graphs, Math. Comput. Sci., 9 (2015), 161-167. doi: 10.1007/s11786-015-0221-5
[15]	J. Ivanĉo, S. Jendroî, Total edge irregularity strength of trees, Discussiones Math. Graph Theory, 26 (2006), 449-456. doi: 10.7151/dmgt.1337
[16]	S. Jendroî, J. Miŝkuf, R. Soták, Total edge irregularity strength of complete graph and complete bipartite graphs, Electron. Notes Discrete Math., 28 (2007), 281-285. doi: 10.1016/j.endm.2007.01.041
[17]	P. Jeyanthi, A. Sudha, Total edge irregularity strength of disjoint union of wheel graphs, Electron. Notes Discrete Math., 48 (2015), 175-182. doi: 10.1016/j.endm.2015.05.026
[18]	P. Majerski, J. Przybylo, On the irregularity strength of dense graphs, SIAM J. Discrete Math., 28 (2014), 197-205. doi: 10.1137/120886650
[19]	J. Miškuf, S. Jendroî, On total edge irregularity strength of the grids, Tatra Mt. Math. Publ., 36 (2007), 147-151.
[20]	M. Naeem, M. K. Siddiqui, Total irregularity strength of disjoint union of isomorphic copies of generalized Petersen graph, Discrete Math. Algorithms Appl., 9 (2017), 1750071. doi: 10.1142/S1793830917500719
[21]	F. Pfender, Total edge irregularity strength of large graphs, Discrete Math., 312 (2012), 229-237. doi: 10.1016/j.disc.2011.08.027
[22]	R. W. Putra, Y. Susanti, On total edge irregularity strength of centralized uniform theta graphs, AKCE Int. J. Graphs Combinatorics, 15 (2018), 7-13. doi: 10.1016/j.akcej.2018.02.002
[23]	B. Rajan, I. Rajasingh, P. Venugopal, Metric dimension of uniform and quasi-uniform theta graphs, J. Comput. Math. Sci., 2 (2011), 37-46. doi: 10.22436/jmcs.002.01.05
[24]	I. Rajasingh, S. T. Arockiamary, Total edge irregularity strength of series parallel graphs, Int. J. Pure Appl. Math., 99 (2015), 11-21.
[25]	R. Ramdani, A. N. M. Salman, On the total irregularity strength of some Cartesian product graphs, AKCE Int. J. Graphs Combinatorics, 10 (2013), 199-209.
[26]	F. Salama, On total edge irregularity strength of polar grid graph, J. Taibah Univ. Sci., 13 (2019), 912-916. doi: 10.1080/16583655.2019.1660086
[27]	F. Salama, Exact value of total edge irregularity strength for special families of graphs, An. Univ. Oradea, Fasc. Math., 26 (2020), 123-130.
[28]	F. Salama, Computing the total edge irregularity strength for quintet snake graph and related graphs, J. Discrete Math. Sci. Cryptography, (2021), 1-14. Available from: https://doi.org/10.1080/09720529.2021.1878627.
[29]	M. K. Siddiqui, On edge irregularity strength of subdivision of star S_n, Int. J. Math. Soft Comput., 2 (2012), 75-82.
[30]	I. Tarawneh, R. Hasni, A. Ahmad, M. A. Asim, On the edge irregularity strength for some classes of plane graphs, AIMS Math., 6 (2021), 2724-2731. doi: 10.3934/math.2021166
[31]	M. I. Tilukay, A. N. M. Salman, E. R. Persulessy, On the total irregularity strength of fan, wheel, triangular book, and friendship graphs, Procedia Comput. Sci., 74 (2015), 124-131.
[32]	H. Yang, M. K. Siddiqui, M. Ibrahim, S. Ahmad, A. Ahmad, Computing the irregularity strength of planar graphs, Mathematics, 6 (2018), 150. doi: 10.3390/math6090150

Reader Comments

Your name:*

Email:*
© 2021 the Author(s), licensee AIMS Press. This is an open access article distributed under the terms of the Creative Commons Attribution License (http://creativecommons.org/licenses/by/4.0)