Some Results and Remarks on Harmonic Mean and Mean Cordial Labelings

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 $\le 9$ to be harmonic mean with the restriction of using the floor function of the definition, and labeling all graphs of order $\le 5$ 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.