The median function on median graphs and semilattices

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Abstract

A median of a k-tuple π=(x1,...,xk) of vertices of a finite connected graph G is a vertex x for which ∑i=1kd(x,xi) is minimum, where d is the geodesic metric on G. The function M with domain the set of all k-tuples with k>0 and defined by M(π)={x|x is a median of π} is called the median function on G. In this paper a new characterization of the median function is given for G a median graph. This is used to give a characterization of the median function on median semilattices. © 2000 Elsevier Science B.V.

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McMorris, F. R., Mulder, H. M., & Powers, R. C. (2000). The median function on median graphs and semilattices. Discrete Applied Mathematics, 101(1–3), 221–230. https://doi.org/10.1016/S0166-218X(99)00208-5

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