Algorithmic upper bounds for graph geodetic number
Data Structures and Algorithms
2020-11-24 v1
Abstract
Graph theoretical problems based on shortest paths are at the core of research due to their theoretical importance and applicability. This paper deals with the geodetic number which is a global measure for simple connected graphs and it belongs to the path covering problems: what is the minimal-cardinality set of vertices, such that all shortest paths between its elements cover every vertex of the graph. Inspired by the exact 0-1 integer linear programming formalism from the recent literature, we propose a new methods to obtain upper bounds for the geodetic number in an algorithmic way. The efficiency of these algorithms are demonstrated on a collection of structurally different graphs.
Cite
@article{arxiv.2011.10989,
title = {Algorithmic upper bounds for graph geodetic number},
author = {Ahmad T. Anaqreh and Boglarka G. -Toth and Tamas Vinko},
journal= {arXiv preprint arXiv:2011.10989},
year = {2020}
}