In this paper, we defined a new graph entropy which is called level entropy. There are some level based entropy measures in the literature. Then, we obtain some relations between the level entropy and other level based entropy measures for rooted trees. Moreover, we obtain that level entropy is less than or equal to Wiener entropy of a rooted tree, if the root vertex of this tree is one of the most distant vertices to any vertex.
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Bünyamin Şahin (2025) studied this question.
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