Some Results and Remarks on Harmonic Mean and Mean Cordial Labelings

M.A. Seoud1, M.A. Salim1
1Department of Mathematics, Faculty of Science, Ain Shams University Abbassia, Cairo, Egypt

Abstract

We give more results in mean cordial and harmonic mean labelings, such as: upper bounds for the number of edges of graphs of given orders for both labelings with direct results, labeling all trees of order \(\leq 9\) to be harmonic mean with the restriction of using the floor function of the definition, and labeling all graphs of order \(\leq 5\) that are harmonic mean graphs without using the label \(q + 1\) in labeling the vertices. Also, we give mean cordial labelings for some families of graphs.