DeepAI AI Chat
Log In Sign Up

Eccentricity function in distance-hereditary graphs

by   Feodor F. Dragan, et al.
Kent State University

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) > rad(G) + 1 has a neighbor with smaller eccentricity. Here, rad(G) = min{e(v) : v ∈ V } is the radius of graph G. Moreover, we use this result to characterize the centers of distance-hereditary graphs and provide a linear time algorithm to find a large subset of central vertices, and in some cases, all central vertices. We introduce two new algorithmic techniques to approximate all eccentricities in distance-hereditary graphs, including a linear time additive 1-approximation.


page 1

page 2

page 3

page 4


Fast approximation of centrality and distances in hyperbolic graphs

We show that the eccentricities (and thus the centrality indices) of all...

Computing Optimal Assignments in Linear Time for Graph Matching

Finding an optimal assignment between two sets of objects is a fundament...

Eccentricity terrain of δ-hyperbolic graphs

A graph G=(V,E) is δ-hyperbolic if for any four vertices u,v,w,x, the tw...

Distance problems within Helly graphs and k-Helly graphs

The ball hypergraph of a graph G is the family of balls of all possible ...

A linear-time algorithm and analysis of graph Relative Hausdorff distance

Graph similarity metrics serve far-ranging purposes across many domains ...

On the computational complexity of the Steiner k-eccentricity

The Steiner k-eccentricity of a vertex v of a graph G is the maximum Ste...

Isometric Hamming embeddings of weighted graphs

A mapping α : V(G) → V(H) from the vertex set of one graph G to another ...