A New Notion of Classical Mean Graphs Based on Duplicating Operations

Abstract

Classical mean labeling of a graph $G$ with $p$ vertices and $q$ edges is an injective function from the vertex set of $G$ to the set $\left\{\mathrm{1,2,3},\dots ,q+1\right\}$ such that the edge labels obtained from the flooring function of the average of mean of arithmetic, geometric, harmonic, and root square of the vertex labels of each edge’s end vertices is distinct, and the set of edge labels is $\left\{\mathrm{1,2,3},\dots ,q\right\}$ . One of the graph operations is to duplicate the graph. The classical meanness of graphs formed by duplicating an edge and a vertex of numerous standard graphs is discussed in this study.