On extremal leaf status and internal status of trees

08/02/2020

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by   Haiyan Guo, et al.

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For a vertex u of a tree T, the leaf (internal, respectively) status of u is the sum of the distances from u to all leaves (internal vertices, respectively) of T. The minimum (maximum, respectively) leaf status of a tree T is the minimum (maximum, respectively) leaf statuses of all vertices of T. The minimum (maximum, respectively) internal status of a tree T is the minimum (maximum, respectively) internal statuses of all vertices of T. We give the smallest and largest values for the minimum leaf status, maximum leaf status, minimum internal status, and maximum internal status of a tree and characterize the extremal cases. We also discuss these parameters of a tree with given diameter or maximum degree.