1. Eccentricity function in distance-hereditary graphs.
- Author
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Dragan, Feodor F. and Guarnera, Heather M.
- Subjects
- *
ALGORITHMS , *RADIUS (Geometry) , *DISTANCES - Abstract
A graph G = (V , E) is distance hereditary if every induced path of G is a shortest path. In this paper, we show that the eccentricity function e (v) = max { d (v , u) : u ∈ V } in any distance-hereditary graph G is almost unimodal, that is, every vertex v with e (v) > r a d (G) + 1 has a neighbor with smaller eccentricity. Here, r a d (G) = min { e (v) : v ∈ V } is the radius of graph G. Moreover, we use this result to fully characterize the centers of distance-hereditary graphs. Several bounds on the eccentricity of a vertex with respect to its distance to the center of G or to the ends of a diametral path are established. Finally, we propose a new linear time algorithm to compute all eccentricities in a distance-hereditary graph. [ABSTRACT FROM AUTHOR]
- Published
- 2020
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