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01-Applied Mathematics & Information Sciences
An International Journal


Volumes > Volume 9 > No. 1


Entire Labeling of Plane Graphs

PP: 263-267
Martin Bača, Stanislav Jendroī, Kumarappan Kathiresan, Kadarkarai Muthugurupackiam,
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.

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