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Complexity of subdivision-vertex and subdivision-edge join graphs

Abstract The entropy of a graph is an information-theoretic quantity which expresses the complexity of a graph. The generalized graph entropies result from applying information measures to a graph using various schemes for defining probability distributions over the elements of the graph. In this paper, the first Zagreb index of a class of composite graphs, namely, subdivision-vertex and subdivision-edge join graphs are investigated in order to evaluate the generalized graph entropies, and explicit formulae for the generalized graph entropy of subdivision-vertex and subdivision-edge join graphs are presented.