A Survey of Irregularity Strength

Abstract This survey aims to give an overview of the modifications of the well-known irregular assignments, namely edge irregular labelings, vertex irregular and edge irregular total labelings, and face irregular entire labelings of graphs.

[1]  Marcin Anholcer Irregular Labellings of Circulant Graphs , 2011 .

[2]  Richard H. Schelp,et al.  Irregular networks, regular graphs and integer matrices with distinct row and column sums , 1989, Discret. Math..

[3]  Muhammad Kamran Siddiqui,et al.  On Edge Irregular Total Labeling of Categorical Product of Two Cycles , 2013, Theory of Computing Systems.

[4]  Ali Ahmad,et al.  On vertex irregular total labelings , 2013, Ars Comb..

[5]  Cory Palmer,et al.  Irregular labelings of circulant graphs , 2012, Discret. Math..

[6]  Muhammad Kamran Siddiqui,et al.  Total edge irregularity strength of strong product of two paths , 2012, Ars Comb..

[7]  Stanislav Jendrol',et al.  Total edge irregularity strength of complete graphs and complete bipartite graphs , 2010, Discret. Math..

[8]  Ali Ahmad,et al.  Total edge irregularity strength of a categorical product of two paths , 2014, Ars Comb..

[9]  Piotr Majerski,et al.  On the Irregularity Strength of Dense Graphs , 2014, SIAM J. Discret. Math..

[10]  Kumarappan Kathiresan,et al.  Entire Labeling of Plane Graphs , 2015 .

[11]  Jakub Przybylo,et al.  A new upper bound for the total vertex irregularity strength of graphs , 2009, Discret. Math..

[12]  Ali Ahmad,et al.  On edge irregularity strength of graphs , 2014, Appl. Math. Comput..

[13]  Khandoker Mohammed Mominul Haque Irregular Total Labellings of Generalized Petersen Graphs , 2011, Theory of Computing Systems.

[14]  Xuding Zhu,et al.  Entire colouring of plane graphs , 2011, J. Comb. Theory, Ser. B.

[15]  Eberhard Triesch,et al.  Irregular Assignments of Trees and Forests , 1990, SIAM J. Discret. Math..

[16]  Florian Pfender,et al.  A New Upper Bound for the Irregularity Strength of Graphs , 2011, SIAM J. Discret. Math..

[17]  Olivier Togni,et al.  Irregularity strength of trees , 1998, Discret. Math..

[18]  Tom Bohman,et al.  On the irregularity strength of trees , 2004 .

[19]  Till Nierhoff A Tight Bound on the Irregularity Strength of Graphs , 2000, SIAM J. Discret. Math..

[20]  Muhammad Kamran Siddiqui,et al.  Total edge irregularity strength of generalized prism , 2014, Appl. Math. Comput..

[21]  Florian Pfender,et al.  On graph irregularity strength , 2002 .

[22]  Dieter Rautenbach,et al.  On a conjecture about edge irregular total labelings , 2008 .

[23]  Jakub Przybylo,et al.  Total Vertex Irregularity Strength of Dense Graphs , 2014, J. Graph Theory.

[24]  Jakub PrzybyŁo Linear Bound on the Irregularity Strength and the Total Vertex Irregularity Strength of Graphs , 2008 .

[25]  Stanislav Jendrol',et al.  On irregular total labellings , 2007, Discret. Math..

[26]  Stanislav Jendrol',et al.  Total edge irregularity strength of trees , 2006, Discuss. Math. Graph Theory.

[27]  Ali Ahmad,et al.  Total vertex irregularity strength of certain classes of unicyclic graphs , 2014 .