Abstract
We continue studying extremal values of the degree-entropy, which is an information-theoretic measure defined as the Shannon entropy based on the information functional involving vertex degrees. For a graph with a given number of vertices and edges achieving the minimum entropy value, we show its unique structure. Also, a tight lower bound for the entropy in bipartite graphs with a given number of vertices and edges is proved. Our result directly derive the result of Cao et al. (2014) that for a tree with a given number of vertices, the minimum value of the entropy is attained if and only if the tree is the star.
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