The Mean Labeling of Some Crowns

Authors

1 Department of Mathematics, Benha Univeristy, El-Shaheed Farid Nada, Banha, Qalyubia 13511, Egypt

2 Department of Mathematics, Clayton State University, Morrow, Georgia 30260, USA

3 Department of Mathematics, Clayton State University, Morrow, Georgia 30260, USA.

Abstract

Mean labelings are a type of additive vertex labeling. This labeling assigns non-negative integers to the vertices of a graph in such a way that all edge-weights are different, where the weight of an edge is defined as the mean of the end-vertex labels rounded up to the nearest integer. In this paper we focus on mean labelings of some graphs that are the result of the corona operation. In particular we prove the existence of mean labelings for graphs of the form G ⊙ mK1 in the cases where G is an even cycle or G is an α-mean graph of odd size and the cardinalities of its stable sets differ by at most one unit. Under these conditions, we prove that G ⊙ P2 and G ⊙ P3 are also mean graphs, and that the class of α-graphs is equivalent to the class of α-mean graphs.

Keywords