On pitfalls in computing the geodetic number of a graph

被引：6
|
作者：
Hansen, Pierre [1 ,2 ]
van Omme, Nikolaj [3 ,4 ]
机构：
[1] Gerad, Montreal, PQ, Canada
[2] HEC Montreal, Montreal, PQ, Canada
[3] CRT, Montreal, PQ, Canada
[4] Ecole Polytech, Montreal, PQ H3C 3A7, Canada
来源：
OPTIMIZATION LETTERS | 2007年 / 1卷 / 03期
关键词：
Graph; Geodetic number; Maximal geodetic closure; Algorithm;
D O I：
10.1007/s11590-006-0032-3
中图分类号：
C93 [管理学]; O22 [运筹学];
学科分类号：
070105 ; 12 ; 1201 ; 1202 ; 120202 ;
摘要：
Given a simple connected graph G = (V, E) the geodetic closure I[S] subset of V of a subset S of V is the union of all sets of nodes lying on some geodesic (or shortest path) joining a pair of nodes v(k), v(l) epsilon S. The geodetic number, denoted by g(G), is the smallest cardinality of a node set S* such that I[S*] = V. In "The geodetic number of a graph", [Harary et al. in Math. Comput. Model. 17: 89-95, 1993] propose an incorrect algorithm to find the geodetic number of a graph G. We provide counterexamples and show why the proposed approach must fail. We then develop a 0-1 integer programming model to find the geodetic number. Computational results are given.
引用
收藏
页码：299 / 307
页数：9
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