Generalized centrality in trees

Martyn Mulder, M.J. Pelsmajer and K.B. Reid

No EI 2006-16, Econometric Institute Research Papers from Erasmus University Rotterdam, Erasmus School of Economics (ESE), Econometric Institute

Abstract: In 1982, Slater defined path subgraph analogues to the center, median, and (branch or branchweight) centroid of a tree. We define three families of central substructures of trees, including three types of central subtrees of degree at most D that yield the center, median, and centroid for D = 0 and Slater's path analogues for D = 2. We generalize these results concerning paths and include proofs that each type of generalized center and generalized centroid is unique. We also present algorithms for finding one or all generalized central substructures of each type.

Date: 2006-04-18
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