Entire Labeling of Plane Graphs

Authors

Martin Bača, Department of Appl. Mathematics and Informatics, Technical University, Letn´a 9, Koˇsice, Slovak RepublicFollow
Stanislav Jendroī, Institute of Mathematics, P.J.ˇSaf´arik University, Jesenn´a 5, Koˇsice, Slovak RepublicFollow
Kumarappan Kathiresan, Department of Mathematics, AYYA Nadar Janaki Ammal College, Sivakasi, 626 124, IndiaFollow
Kadarkarai Muthugurupackiam, Department of Mathematics, Rajah Serfoji Government College, Thanjavur, 613 005, IndiaFollow

Author Country (or Countries)

Slovak Republic

Abstract

A face irregular entire k-labeling j : V ∪E ∪F →{1,2, . . . , k} of a 2-connected plane graph G = (V,E,F) is a labeling of vertices, edges and faces of G in such a way that for any two different faces f and g their weights wj ( f ) and wj (g) are distinct. The weight of a face f under a k-labeling j is the sum of labels carried by that face and all the edges and vertices incident with the face. The minimum k for which a plane graph G has a face irregular entire k-labeling is called the entire face irregularity strength. We investigate a face irregular entire labeling as a modification of the well-known vertex irregular and edge irregular total labelings of graphs. We obtain some estimations on the entire face irregularity strength and determine the precise values for graphs from three families of plane graphs.

Digital Object Identifier (DOI)

http://dx.doi.org/10.12785/amis/090132

Recommended Citation

Bača, Martin; Jendroī, Stanislav; Kathiresan, Kumarappan; and Muthugurupackiam, Kadarkarai (2015) "Entire Labeling of Plane Graphs," Applied Mathematics & Information Sciences: Vol. 09: Iss. 1, Article 39.
DOI: http://dx.doi.org/10.12785/amis/090132
Available at: https://digitalcommons.aaru.edu.jo/amis/vol09/iss1/39