Geodesic
On Face Irregular Evaluations of Plane Graphs
Discussiones Mathematicae. Graph Theory, Tome 42 (2022) no. 2, pp. 549-568.

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We investigate face irregular labelings of plane graphs and we introduce new graph characteristics, namely face irregularity strength of type (α,β,γ). We obtain some estimation on these parameters and determine the precise values for certain families of plane graphs that prove the sharpness of the lower bounds.
Keywords: plane graphs, irregular assignment, irregularity strength, face irregular labeling, face irregularity strength 
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Bača, Martin; Ovais, Ali; Semaničová-Feňovčíková, Andrea; Suparta, I. Nengah. On Face Irregular Evaluations of Plane Graphs. Discussiones Mathematicae. Graph Theory, Tome 42 (2022) no. 2, pp. 549-568. http://geodesic.mathdoc.fr/item/DMGT_2022_42_2_a12/

[1] A. Ahmad, O.B.S. Al-Mushayt and M. Bača, On edge irregularity strength of graphs, Appl. Math. Comput. 243 (2014) 607–610. https://doi.org/10.1016/j.amc.2014.06.028

[2] A. Ahmad, M. Bača and M.K. Siddiqui, On edge irregular total labeling of categorical product of two cycles, Theory Comput. Syst. 54 (2014) 1–12. https://doi.org/10.1007/s00224-013-9470-3

[3] M. Anholcer, M. Kalkowski and J. Przybyło, A new upper bound for the total vertex irregularity strength of graphs, Discrete Math. 309 (2009) 6316–6317. https://doi.org/10.1016/j.disc.2009.05.023

[4] M. Anholcer and C. Palmer, Irregular labelings of circulant graphs, Discrete Math. 312 (2012) 3461–3466. https://doi.org/10.1016/j.disc.2012.06.017

[5] F. Ashraf, M. Bača, Z. Kimáková and A. Semaničová-Feňovčíková, On vertex and edge H - irregularity strengths of graphs, Discrete Math. Algorithms Appl. 8 (2016) 1650070. https://doi.org/10.1142/S1793830916500701

[6] F. Ashraf, M. Bača, M. Lascsáková and A. Semaničová-Feňovčíková, On H-irregularity strength of graphs, Discuss. Math. Graph Theory 37 (2017) 1067–1078. https://doi.org/10.7151/dmgt.1980

[7] F. Ashraf, M. Bača, A. Semaničová-Feňovčíková and M.K. Siddique, On H-irregularity strength of ladders and fan graphs, AKCE Int. J. Graphs Comb. 17 (2020) 213–219. https://doi.org/10.1016/j.akcej.2019.04.002

[8] M. Bača, S. Jendrol’, K. Kathiresan and K. Muthugurupackiam, Entire labeling of plane graphs, Appl. Math. Inf. Sci. 9 (2015) 263–267. https://doi.org/10.12785/amis/090132

[9] M. Bača, S. Jendrol’, K. Kathiresan, K. Muthugurupackiam and A. Semaničová-Feňovčíková, A survey of irregularity strength, Electron . Notes Discrete Math. 48 (2015) 19–26. https://doi.org/10.1016/j.endm.2015.05.004

[10] M. Bača, S. Jendrol’, M. Miller and J. Ryan, On irregular total labellings, Discrete Math. 307 (2007) 1378–1388. https://doi.org/10.1016/j.disc.2005.11.075

[11] M. Bača and M.K. Siddiqui, Total edge irregularity strength of generalized prism, Appl. Math. Comput. 235 (2014) 168–173. https://doi.org/10.1016/j.amc.2014.03.001

[12] G. Chartrand, M. S. Jacobson, J. Lehel, O.R. Oellermann, S. Ruiz and F. Saba, Irregular networks, Congr. Numer. 64 (1988) 187–192.

[13] A. Frieze, R.J. Gould, M. Karoński and F. Pfender, On graph irregularity strength, J. Graph Theory 41 (2002) 120–137. https://doi.org/10.1002/jgt.10056

[14] J. Ivančo and S. Jendrol’, Total edge irregularity strength of trees, Discuss. Math. Graph Theory 26 (2006) 449–456. https://doi.org/10.7151/dmgt.1337

[15] S. Jendrol’, J. Miškuf and R. Soták, Total edge irregularity strength of complete graphs and complete bipartite graphs, Discrete Math. 310 (2010) 400–407. https://doi.org/10.1016/j.disc.2009.03.006

[16] M. Kalkowski, M. Karoński and F. Pfender, A new upper bound for the irregularity strength of graphs, SIAM J. Discrete Math. 25 (2011) 1319–1321. https://doi.org/10.1137/090774112

[17] P. Majerski and J. Przybyło, Total vertex irregularity strength of dense graphs, J. Graph Theory 76 (2014) 34–41. https://doi.org/10.1002/jgt.21748

[18] P. Majerski and J. Przybyło, On the irregularity strength of dense graphs, SIAM J. Discrete Math. 28 (2014) 197–205. https://doi.org/10.1137/120886650

[19] K.M.M. Haque, Irregular total labellings of generalized Petersen graphs, Theory Comput. Syst. 50 (2012) 537–544. https://doi.org/10.1007/s00224-011-9350-7

[20] K. Muthugurupackiam, Total face irregularity strength of plane graphs, J. Graph Label. 2 (2016) 69–77.

[21] Nurdin, E.T. Baskoro, A.N.M. Salman and N.N. Gaos, On the total vertex irregularity strength of trees, Discrete Math. 310 (2010) 3043–3048. https://doi.org/10.1016/j.disc.2010.06.041

[22] J. Przybyło, Linear bound on the irregularity strength and the total vertex irregularity strength of graphs, SIAM J. Discrete Math. 23 (2009) 511–516. https://doi.org/10.1137/070707385