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# Logarithmic Mean Labeling of Some Ladder Related Graphs

## Abstract

In general, the logarithmic mean of two positive integers need not be an integer. Hence, the logarithmic mean is to be an integer; we use either flooring or ceiling function. The logarithmic mean labeling of graphs have been defined in which the edge labels may be assigned by either flooring function or ceiling function. In this, we establish the logarithmic mean labeling on graphs by considering the edge labels obtained only from the flooring function. A logarithmic mean labeling of a graph G with q edges is an injective function from the vertex set of G to 1, 2, 3,..., q+1 such that the edge labels obtained from the flooring function of logarithmic mean of the vertex labels of the end vertices of each edge are all distinct, and the set of edge labels is 1, 2, 3,..., q. A graph is said to be a logarithmic mean graph if it admits a logarithmic mean labeling. In this paper, we study the logarithmic meanness of some ladder related graphs.

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